Managing colombian farmers price risk exposure with electrical derivatives market

Abstract

Food security is among the most pressing global concerns. It is principally threatened by the combination of rural migration and the pressure of climate change. In order to mitigate these effects, the need to promote stable conditions for small producers -who generate 80% of the world's food- has arose. In search to improve market conditions, this study aims to evaluate the feasibility of cross-hedging between electrical derivatives market and spot agricultural products in Colombia. This hypothesis is proposed, as Colombia depends upon hydro-electricity, an electricity source which is heavily influenced by climatic conditions, particularly the “El Niño” southern oscillation (ENSO). The prices of agricultural products are thus volatile, and subject to this phenomenon. ENSO is presumed to be an important link between these two markets. To contrast the hypothesis, the most commonly- methods in cross-hedging literature were employed to estimate hedge ratios: OLS, Error Correction Models, and GARCH estimations. This last estimation was found to be the one with the best performance for hedge ratio estimation. Despite this, of 93 products analyzed, statistically significant relationships were found for only nine. Besides, it was found that cross-hedging contributes to a risk reduction of not more than 32%.

Agriculture cross-hedging; Agriculture risk management; Sustainable risk management; Price risk exposure; Food security; Agricultural economics; Econometrics; Food economics; Risk management

1. Introduction

The sustainable development goal (SDG) 2: Zero Hunger, established the global need to strengthen food security. Phenomena such as rural migration, the pressure of climate change on crops and water scarcity are the main elements that put food security at risk. Despite being phenomena of different dimensions, it has been shown that the three phenomena can interact to reinforce their levels of appearance. For example, in India, it was found that the elasticity of per capita agriculture income was -0.775 with respect to migratory flows to urban centers (Viswanathan & Kavi Kumar, 2015). The same study found that a 1% decline in crop yields in an area generates a 2% increase in the migration rate. Since 2015, SDGs have sought to raise humanity's awareness of the need to change. However, countries that have the potential to be global food suppliers have not implemented effective measures to fight these phenomena that undermine food security (Battersby, 2017).

As a response to this concerns, this paper evaluates the feasibility of resorting to the Colombian power market to mitigate the exposure to price risk to which the growers are exposed, by means of cross-hedging with the electricity sector. The reason for proposing this alternative underlies three elements of this market. Firstly, the dependence of Colombia's national electricity generation system (NEGS) on hydroelectric plants. 68% of its installed capacity comes from hydraulic generation through reservoirs. Between 77% and 80% of electricity is produced in hydraulic plants, becoming 92% in strong rainy conditions and 61% in intense dry conditions. This dependence causes climatic phenomena to affect the performance of the system, which is reflected in power prices (Julio & María Jimena Córdoba de la, 2008; Velasquez et al., 2015). This dependence is exacerbated especially with climatic phenomena typical of the tropics, such as El Niño Southern Oscillation (ENSO, aka “El niño”). The literature documents how ENSO has legible effects on the prices of agricultural products, as well as their variability (Hansen et al., 1998; Henson et al., 2017; Mauget et al., 2009). This is why the existence of a relationship in the variability and performance of the prices of both markets is presumed.

Secondly, since October 2010 there is a market for derivatives of futures contracts on the price of electricity produced. This market has evolved from offering contracts with monthly expiration, to offering contracts with expiration in each of the following 12 months (Velasquez et al., 2015). Due to the volatility of the market, there is concurrence from the supply side by 44 agents, and from the supply side by 93 marketers. This, together with a national demand of 69,129 GWh, which generates negotiations 24 h a day, makes it a market with high liquidity conditions for its participants. This liquidity condition is an important element to ensure that the hedge is effective (Lien, 2003).

Thirdly, the structure of future contracts that are traded. The futures market offers two standardized contracts that are identical in their conditions, except for the amount of the underlying asset traded. The largest contract trades the equivalent of 360,000 kWh, while the smallest, 10,000 kWh. This, in addition to the fact that the market allows at least 1 contract to be traded, means that the market requires, for the contract, a capital of approximately USD 366 (calculated with respect to the average price of the underlying asset in 2018) plus the margin deposit (which depends on the term of the contract, but the highest is 21% on the value of the contract and it is refundable). This element is very important, because the willingness to pay for hedging is an important element to be considered by the small farmer (Blank, 1992; Seth et al., 2009).

This study is relevant because it seeks to contribute to Farmers and Policymakers in a pragmatic way to use existing markets to reduce price-risk exposure of agricultural commodities. In Colombia this pragmatic approach is required due to the fact that each year' COP 7 billion (roughly USD 1,9 Billions) are destined as subsidies to farmers. Those resources are not used to afford technical assistance, capital investment or technological improvement. 92% of those resources are used to aid farmers to overcome loses due to overproduction, climate related phenomena (floods, droughts, plague and similars) or price risk. Findings of this study could lead to trade the risks faced by farmers and hedged with subsidies to an existing market. This could lead to explore how to reallocate those yearly USD 1,9 Billions in technical assistance to provide training and technology, instead of a ex-post mitigation. This contribution could lead to strength food security in Colombia.

Also, considering that climate change generates a reduction in crop yields (Cammarano et al., 2016) -especially in lower-income countries (Hertel and Rosch, 2010), an increase in price volatility, as well as an increase in the risk of loss due to extreme weather events (Cammarano et al., 2016). This study helps to explore cross-hedging price risk in an existing financial market as a temporal tool to mitigate climate change consequences. For example, strategies to improve Farmers' income. This is important given that it has been proved to be an effective way to poverty decrease (Kurukulasuriya et al., 2006). This reduction reinforces the phenomenon of rural migration, and therefore weakens local and global food security. Moreover, not only does it harm SDG 2, but it impairs compliance with SDG 1 and 8, poverty and economic growth, which are also harmed by this dynamic (Hertel and Rosch, 2010). Another repercussion of this research, it is the reduction in the gap of financial inclusion of base of pyramid populations (BoP). Reduction in affordability barriers thorough public policy have been showed to be an effective way to include this populations (Aiyar and Venugopal, 2020). This study seeks to provide some foundations of such that public policy. For these reasons, solutions which provide farmers with tools to overcome risks as entrepreneurs, are required to prevent migrations due to lack of opportunities. This study explores this kind of solutions.

The World Bank has documented how investment in agriculture, where small farmers are encouraged to participate as entrepreneurs in a market, has twice the impact on poverty reduction. Therefore, working on strategies that allow to assist the small farmer and stabilize their market conditions are important to counteract rural migration and contribute to the achievement of SDGs 1, 2 and 8. According to the UN, the strategies that are proposed must be focused on generating adaptation or sustainable mitigation of the effects caused by climate change. These options must include solutions that consider the risks associated with climate, and include crop insurance systems (Harvey et al., 2014).

One of the biggest challenges facing the modern grower is unexpected changes, extreme price up/down movements, which have become more frequent and common. These sudden changes in agricultural product prices generate undesirable events not only for the farmer, but also for policy makers (Mergos and Papanastassiou, 2017). To mitigate this volatility, there are crop insurance and even subsidies for these insurance premiums. However, access to these insurances has high acquisition, management costs (typically cultivation areas are far from insurers), high systemic risks, agency problems as well as high costs associated with the contract due to moral hazard and adverse selection (Vedenov and Barnett, 2004). An example of this situation is the experience of Colombia, a country with high agricultural potential, but with limitations to ensure its agricultural production. For the four-year period from 2014 to 2018, resources equivalent to USD 52 million (the equivalent of 0.2% of one year of agricultural production) were allocated to subsidize crop insurance premiums. These resources were used to meet the equivalent of 3% of the agricultural area of the country. In the same period, insurers had to pay for claims the equivalent in local currency to USD 87.3 million.

Other existing options for financial hedging in the agricultural sector are climate derivatives. The literature is rich in the development of theoretical models for the structuring and valuation of crop insurance, as well as in the proposal of climate derivatives. However, the application of these works to real conditions has occurred only in developed countries. Developing countries, who are the ones that most need these instruments, do not have the financial or administrative capacity to develop them in the short or medium term. Another strategy for managing financial risk in agricultural products is crop diversification. This is not a greater option than insurance or derivatives, since in addition to requiring significant additional capital, it implies the ability to have more land and resources, which is not common with small farmers. In this way, to achieve an effective intervention in the medium term, pragmatic options are required that take advantage of existing resources and consider the conditions of each region.

The academic literature dedicated to cross-hedging is extensive and has an important history. From Anderson's first developments in 1981 (Anderson and Danthine, 1981) that made approximations through mean-variance models to Ankirchner's deep econometric work that includes the basis risk and supposes a stochastic structure of the correlation (Ankirchner and Heyne, 2012). The majority of these works have focused on addressing problems related to currency, stock and commodities markets (Adams and Gerner, 2012; Chang and Wong, 2003; Wong, 2017). Cross-hedging in the agricultural sector has also been an issue addressed by the literature (since 1985 with Miller (Miller, 1985)), however, it has not been a subject worked with the same intensity as the stock market. The approach used in this study was to collect monthly data of prices of 88 agricultural products from 2009 to 2019 (products to be hedged) and data of derivatives contracts of electricity with hedging horizons of one to six months (contracts to be used to cross-hedge agricultural commodities). The data was used to estimate cross-hedging ratio with regression models that account for lagged relations, heteroscedasticity in residuals and cointegrated series. Given that one of the hypothesis and motivations of this study is that agricultural and electricity markets are integrated due to the influence of climate, an ENSO index is included to account for this relation on both markets. Only for 23 agri-products showed statistical significance and the GARCH approach showed to be the more robust and statistically effective. Results show low effectivity on the cross-hedging strategies ranging from 15% to 40% of effectiveness (measure by R-squared). A robustness check through a back-ward evaluation showed only a 32% of risk reduction.

The relevance of carrying out this work applied to Colombia lies in its natural potential to strengthen global food security. Colombia has the natural resources and conditions for the development of agribusinesses that contribute to the global food supply (Correa, 2004). In contrast to this potential, the country has a series of deficiencies that prevent its development, among them, it lacks effective instruments to achieve an appropriate risk management in agriculture. Between 2010 and 2017, USD 250 million were allocated to serve agricultural producers affected by climatic phenomena. The public policy strategy for the integral management of agricultural risks in Colombia established that for the 2018 to 2022 period it is necessary to: i) increase the allocation of resources in programs that reduce agricultural sector vulnerabilities, while reducing the concentration in the insurance subsidy; ii) focus and encourage the development of risk transfer mechanisms and iii) reduce the effects of price variability on agricultural products (Buitrago et al., 2018). One of the aims of this study is to explore market mechanisms to deal with risk exposure of Colombian farmer. So, this research pretend to pave the way in Colombia to explore relations with other markets as Colombian Stock and Fix income markets, as well as other commodities markets as Gold, Currency, Oil and Bio-fuels as other researchers has proposed. Also, this study pretend to encourage research to reallocate agricultural subsidies in better uses that promote Farmers as entrepreneurs, and not as precarious producers. As showed, results are not promising, only a 32% reduction, but lead to explore results with more refined data, as one with daily or weekly periodicity. Also, the variable used to account for ENSO effect was one measured for a general region, and not for specific productions regions which also could improve cross-hedging ratios estimates and performance. The fact that some statistical significance was found lead to consider that hypothesis explored in this paper could be refined to find implement the solutions implied in the hypothesis. Robustness check estimations of OHR was made with help of autoregressive models (VAR and GARCH family) to test statistical evidence for cross-hedging. Result obtained are mixed, with a majority showing low feasibility in the way we developed our model.

The remainder of this article is organized as follows. The following section presents an overview and current status of cross-hedging, especially in the agricultural sector, as well as a description of the most commonly used techniques for structuring hedging. The third section describes the data used for the hedging evaluation, as well as the evaluation made of the cross hedging in time horizons between 1 and 6 months. The fourth section discusses the results found and the discussion regarding studies in the same area, as well as the hypothesis we are working on.

2. Literature review and description of the methodology

2.1. Agricultural Risk Management and climate change

One of the main characteristics of agriculture is the high levels of risk that it entails (Velandia et al., 2009). Farmers face threats from the necessary supplies to develop their activity (pests, diseases, characteristics of the crop), commercial conditions (fluctuating raw material costs, uncertain marketing prices) and the impact of these on their finances (debts repayment capacity and stability of income) (Isakson, 2015b). The existence of the inherent risks in agriculture is not something new for humanity; we have successfully mitigated and managed them for generations (Farzaneh et al., 2017). However, the processes of globalization and growth have caused that the effective management of the risks associated with agriculture takes on great importance due to the threat they pose to the world's food security (Torquebiau et al., 2016).

The exacerbated presence of risks in agriculture in the productive, marketing and financial dimensions has strongly encouraged the development of strategies, methods and tools to confront these risks. This set of techniques is what has given rise to Agricultural Risk Management (ARM). The approaches that ARM has generated to deal with the risks associated with agriculture range from the appropriate selection of supplies (seeds, fertilizers), land preparation (soil enrichment with nutrients, technical and technological improvements), best practices (disease controls) to elements such as the use of financial instruments such as crop insurance, financial hedging strategies or diversification of production in different crops (Velandia et al., 2009). Although the study techniques addressed by the ARM tackle different disciplines, all approaches consider climate as a central element in the study of risks and their management.

Research and studies in ARM have considered climate as a central variable when studying risks and their effects. Thus, the studies have focused on two aspects. The first and most obvious is that the climate is changing as a consequence of anthropogenic processes that have brought and will bring unpredictable changes in climate (Solomon & Intergovernmental Panel on Climate C, 2007). This Climate Change (CCh) in turn have generated and will continue to generate intense changes in the manifestation of the risks associated with agriculture (extreme temperatures, disease propagation, extreme fluctuations in prices, and deterioration in the quality of the products, among others) and likewise they have precipitated the appearance of other emerging risks. Along these lines, the study and research, aimed at dealing with and proposing solutions to mitigate and manage climate change, have led to what we will call the adaptive response from the ARM. This approach seeks to create strategies to face the possibilities derived from changes in climate with a flexible risk-based approach and be able to cope with the spectrum of possibilities that this can create (Howden and Stokes, 2009).

ARM studies have also focused on the mitigation of effects of CCh. This perspective starts from the fact that, although agriculture is affected by the CCh, it in turn contributes to it. Globally, the agricultural sector contributes 24% of greenhouse gas emissions, which cause CCh and the human footprint in climate (Torquebiau et al., 2016). The interest of this aspect is, in addition to recognizing the impact of agricultural activities, to generate measures that prevent climatic conditions from changing and creating scenarios of unknown climate conditions. The efforts put forth from this focus are aimed at producing best practices (use of water, fertilizers and chemicals) to consider the development of supply chains that contribute to the reduction of greenhouse gases (Vehicles allocation).

Despite the academic interest in the ARM and the abundant research on CCh, the application and consideration of this new knowledge is not taken into account in practice by farmers or governments. Actions such as that of the US to withdraw from the Paris agreement are a small sample of the above. To counteract this trend, the UN Food and Agriculture Organization (FAO) has developed the Climate-Smart Agriculture (CSA) approach; “…an approach that helps to guide actions needed to transform and reorient agricultural systems to effectively support development and ensure food security in a changing climate” (FAO, 2013). FAO has established three specific objectives for the CSA: 1) sustainably increasing agricultural productivity to support fair income for producers, generating food security and development, 2) adapting and building resilience of agriculture and food security to climate change at different levels and 3) reducing greenhouse gas emissions produced by agriculture.

The differentiating element of the CSA underlies in three elements. Firstly, it is promoted and supported by the United Nations within the framework of the Sustainable Development Goals (SDG). This is important because it allows promoting and popularizing this approach among countries committed to the SDG. Secondly, in addition to having a conceptual framework, it also directs specific resources allocated for the funding of projects framed in this initiative (Nakhooda et al., 2013). Lastly, it is an integral vision; it incorporates the two main aspects of the ARM (mitigation and adaptation) in a single effort oriented towards the sustainability of food security and agriculture, seeking to put them into practice. Likewise, it serves as an integrative approach to the SDG. Although it might be thought that CSA corresponds to an approach specific to agricultural sciences, it also involves diverse developments such as innovations in the field of climate forecasts, early warning systems (Murray et al., 2016) and financial assurance (Makate et al., 2018).

2.2. Agriculture hedging

2.2.1. World perspective

Farmers, like any company, face risks associated with the production and sale price of the products they grow. To effectively mitigate price risk, they have market instruments such as futures and options contracts, however, to mitigate production risk there are no such market instruments. Instead, in some cases, they have subsidized government programs that partially mitigate these risks through crop insurance (Vukina et al., 1996; Sayinzoga et al., 2016). This last mechanism depends entirely on the government to mitigate the risk, or at least for private companies to participate in risk insurance (Conradt et al., 2015).

In the US, this type of program has evolved to such an extent that, in addition to the derivatives market as an alternative to mitigate price risk, government incentives through subsidies and loss compensation have aroused the interest of the private sector to offer products to ensure the price and the yield of the harvest (Coble et al., 2000). One of the main difficulties of insurance schemes is that, besides requiring subsidies for their existence, they require excessive premiums to mitigate moral hazard or adverse selection biases (Just and Pope, 2003), information asymmetries (Conradt et al., 2015), conflict of interests of the insurer, high transaction costs (Isakson, 2015b) among others. In response to these shortcomings, the assurance has evolved towards the index-based insurance. This scheme is characterized by generating a scheme in which the payments and compensation of the insurance are made based on a general index, instead of a specific event (a specific crop, for example). The index is selected in such a way that a high correlation is generated between the event to hedge and the behavior of the index. Likewise, Glauber states that in comparison to traditional insurance, the use of an index as a compensation mechanism lowers the insurability threshold and at the same time extends the scope to be offered to small growers (Glauber et al., 2002).

Isakson mentioned a greater resemblance of index-based insurance to the derivatives market than to conventional insurance (Isakson, 2015b). This is due to the fact that those involved in the insurance agreement, through an index, bet on the behavior of a general event, rather than on the behavior of the crop. Likewise, the payment structure can lead to a payment being received in the event that the unfavorable event is not suffered or that despite the occurrence of the unfavorable event, no compensation is received. This situation, in which the index differs from the performance of the event that is to be covered, is called the basis risk. This emerging risk due to the use of index-based insurance is one of the main disadvantages of this insurance scheme. Finally, Isakson concludes that in the current context of climatic change and increasing market uncertainty, the rollback of state protections has rendered small-scale farmers, especially marginalized peasant producers in the Global South, particularly vulnerable to these contemporary stressors (Isakson, 2015a).

2.2.2. Current status in Colombia

In Colombia, the general development of a derivatives market is limited and incipient. This has been mainly oriented in the exchange market and interest rates. The weather or crop-based derivatives market does not exist. OTC agreements are stablished between big producers, but small-farmers have no access to these. Despite the lack of a weather derivatives market, this issue has been considered conceptually and theoretically in numerous studies, mainly due to two reasons. On the one hand, about 64% of the Colombian power generation system depends on the generation of hydraulic energy ((UPME), 2019). Therefore, the oscillations caused by ENSO (which decreases and increases rainfall), have strong consequences on this sector (Bedoya-Soto et al., 2019; Poveda et al., 2011). Also, as Colombia has the second highest price in kw-h compared to Latin America it can affect the national productivity. The second cause that may explain the interest of Colombian researchers in this issue may be associated with the fact that according to Weatherbill Colombia ranks 20^th, among 68 countries considered, in terms of weather sensitivity (the possibility of injury, damage or financial loss due to extreme changes), having a capital at risk for this weather sensitivity of USD 26,816 million (1.253% of GDP) (Weatherbill, 2008).

Among the research found, the persistence of a world trend indicated by Vedenov and Barnet stands out (Vedenov and Barnett, 2004). Numerous studies focus on the development of methodologies for the actuarially fair valuation of this type of derivatives, as well as the institutional necessary frameworks for their implementation. That is, the supply side is exhaustively studied. This type of studies correspond to Cruz and Llinas (Cruz & Llinass, 2010), García Soto (García Soto, 2011), Serrano and Rico (Arias et al., 2017), as well as numerous undergraduate and master's theses in Colombia. However, no local studies were found on the demand side, that is potential applications, markets and strategies for ARM.

The unique experience on the implementation of ARM with cross-hedging derivatives was conducted as a shared adventure between the Ministry of Agriculture and Rural Development of Colombia (MADR in Spanish) and the Colombia Mercantile Exchange (BMC in Spanish) to hedge the price of yellow corn. The initiative sought to encourage production by removing the price risk and thus stabilize the income. The program has been carried out since 2011 and continues to date. Here the MADR will facilitate the means for yellow corn producers to acquire American put options that are traded in the CME (Chicago Mercantile Exchange), with the yellow corn price underlying it. As an incentive, a subsidy is provided on the cost of acquiring the option, for up to 80% of the value of the premium. As the operation is performed in foreign currency, accompaniment is also carried out to neutralize the exchange effect and thus be able to set the price in local currency. The BMC acts as financial intermediary of the operation when executing the transactions, as well as the grower's technical advisor in the preparation of the hedging. This program arose because Colombia imports 40% of its yellow corn consumption. This high level of imports, added to the free trade agreements signed by Colombia, means that the price formation is strongly correlated with that of the spot and future price of yellow corn in the CME (yellow corn).

The requirements for access to the program are minimal, however, it is aimed at technified producers. This is a disadvantage, since as mentioned above, one of the biggest shortcomings of the Colombian countryside is its low level of technology, as well as the limited resources devoted to technical training. That is, this feature restricts the scope of the program.

Regarding the second experience, this was developed only by associations of farmers and as a private initiative, without any type of public incentive. This was developed with futures contracts on coffee to fix the price and guarantee the delivery of the commodity. Jaramillo admitted that this experience was not successful due to institutional barriers such as exchange controls, lack of access to credit and financial education to participate in these types of markets (Jaramillo, 2018). It is important to highlight that, except for the authors cited, no studies, reports or other type of document were found that share the experience of both programs.

2.3. Development of cross-hedging and procedures

The academic literature on cross-hedging and its estimation is possible to trace since 1979 with the work of Ederington (1979) and then, with Anderson formally coining the term (Anderson and Danthine, 1981). Regarding the application of cross-hedging for agricultural products, Rolfo since 1981 raised cocoa hedges with the existence of basis risk (Rolfo, 1980), later Witt (Witt et al., 1987) addressed from an analytical approach the possibility of cross-hedging for agricultural producers. In both cases, an Optimal Hedge Ratio (OHR) was required due to the fact that a one to one hedge is not optimal to minimize the variance of the resulting hedging portfolio.

So, as response to the need of a OHR, linear regressions through Ordinary Least Squares (OLS) has been the appropriate way to estimate this parameter with the goal of minimize portfolio volatility. The dependent variable corresponded to the spot price of the asset on which it is desired to mitigate the risk, while the dependent variable corresponded to the price of the future to be covered. Alternatively, the variables were analyzed from their variation. The slope associated with the coefficient of the dependent term corresponded to the estimation of the minimum variance hedge ratio -OHR (Castelino et al., 1991). The representation of these models for this work would take the following form

$$S_t=a+\beta \ast F_{t,T}+{\epsilon }_t$$ (1)

where β corresponds to the minimum variance estimate (MV) for the cross-hedging ratio -or simply the OHR-, S_t corresponds to the spot prices of agricultural products, while $F_{t,T}$corresponds to the price to be established for contracts with maturity in T. And advantage of using a linear regression approach is that the explanatory power of the estimation of this model would indicate the suitability of the electricity futures market for cross-hedging. In this way, if the model had the capacity to explain 100% of the variability of the spot price of the agricultural product, it would be expected that any cost or loss in the spot market would be fully compensated by the gains in the position in the futures contract in the electricity futures market. This means that both the R-squared (R2) or the log-likelihood value of the model estimate are values of interest to measure performance of the hedging portfolio.

In subsequent works, Nelson in the 80's showed that regressions with nonstationary data leads to spurious relations. This finding changed the way optimal cross-hedging ratios were estimated (Nelson and Plosser, 1982). Likewise, Bennigna suggested using transformations with natural logarithms to mitigate the effect of nonstationarity in estimating the cross-hedging ratio (Benninga et al., 1983). Considering these approaches, in the applied part of this study, to avoid errors in OHR estimation due to misspecification of the relationship between of the spot and future prices, the logarithm of the level of spot prices (St) around the logarithm of forward prices for different maturities offered by the Colombian electricity market is also carried out, thus obtaining the following model:

$$log{S}_t=a+\beta log{F}_{t,T}+{\epsilon }_t$$ (2)

Neither Eq. (1) nor (2) recognizes the fact that between futures and spot markets, there is a convergence of future prices towards the spot market at the time the contract expires (Herbst et al., 1993). Ignoring this restriction in modeling leads to the error term (ε_t) having autocorrelation problems and the consequent loss of statistical efficiency in the model estimates. Likewise, working with price series can produce heteroskedasticity in the residuals, because volatility may be time-conditioned (Bollerslev et al., 1992; Engle, 1982). So, to overpass limitations of traditional regression models, more sophisticated methods are explored to deal with possible transgressions to the basic OLS.

After pointing out the statistical shortcomings that could come from ignoring the effects of working with nonstationary, autocorrelated series and with time-conditioned volatility, the academic literature focused on correcting them. In addition to the use of transformations in logarithms such as the aforementioned, statistically more complex developments have been implemented such as Cochrane-Orcutt transformation in the series of prices or generation of autoregressive vectors to deal with autocorrelation (Clark et al., 2003; Lien and Tse, 1999). Also, it has been documented how agricultural product prices (agri-prices) have time-varying variances. This phenomenon occurs due to seasonality, volume traded, open interest, incentives such as subsidies, government promotion of certain crops (Garcia, 2004) interdependences between commodities even if they are not from the same market – oil and wheat-, substitutes -agricultural and energy related commodities- or derived from -sugar and soy-beans (Tsuji, 2020). Due to this phenomenon, studies have generalized the use of models of the ARCH family (GARCH, E-GARCH, M-GARCH) (Ankirchner and Heyne, 2012; Brooks and Chong, 2001; Lien and Luo, 1994) as well as the estimation of the coefficients as if they were dynamic over time or by seasons (Baillie and Myers, 1991; Woo et al., 2011) or the use of techniques to estimate causality among commodities (Chiu et al., 2016). With the use of these estimation methods, authors seek to overcome these characteristics of the agri-prices time series and in general the prices of futures contracts.

Adams and Gerner point out that while it is important to address the statistical shortcomings mentioned, it is preferable to incorporate the existence of a potential long-term equilibrium into modeling (Adams and Gerner, 2012). Consequently, they present how Ghosh and Lien point out that ignoring the existence of a cointegration relationship can lead to an under-hedged position due to the mis-specification of the pricing behavior between the spot and futures market (Fernandez-Perez et al., 2016; Ghosh, 1993). After all, presuming a cointegration relationship articulates considering that in the long term they tend to follow the same trend. To the same extent, they point out that an additional advantage of using cointegration in the estimation of the cross-hedging ratio is that the speed of process adjustment, usually associated with an error correction model (ECM), improves the effectiveness of the hedge. This estimate of the speed of adjustment is important for an agricultural producer or policy-maker as it indicates the time in which prices of the spot market and electricity futures can return to equilibrium, after some disturbance that has put them in trends opposite or divergent. For this work, this relationship is of the utmost importance, since being an exploratory study, the global price ratio (that is, the prices to the end user) has been considered and not the producer prices. Local phenomena such as transport difficulties (which are recurring in developing countries), isolated or regional climatic events may have short-term effects on the relationship's behavior, but be restored in the long term.

When characterizing the series of data considered for the study, we found the presence of autocorrelation and conditioned variability in the time of the residuals. The statistic test used to complete these conditions on the residuals in the estimation of Eqs. (1) and (2) was the LM-test and Breusch-Pagan-Godfrey. To the same extent, we evaluated the cointegration of the spot price series with respect to the prices of futures contracts. In this case, findings produce mixed results; most series show cointegration with futures prices, while a few do not. The Phillips Perron test was used to determine if the residuals of the model represented in Eq. (1) have a unit root, in which case they would not exhibit a cointegration relationship. The statistical tests performed are not included in this paper reasons of space, however, they are available upon request. So, these findings lead to include other statistical models which correct for autocorrelation and conditional variability, to achieve our goal of estimate a OHR with minimal variance. Other common methods as functional transformations or differences of the sport and future prices showed no improved to this condition in a satisfying way (i.e, autocorrelation could be solved but conditional variability remained, or vice versa).

In addition to the previous statistical considerations, the literature has proposed to recognize the explicit presence of exogenous risk factors that affect the performance of the hedge. Woo proposes to realize hedging of electricity spot-price risk in the United States Pacific Northwest with futures of NYMEX natural gas futures, recognizing the presence of temperature and hydro risks. To do this, he includes in the estimation of the MV cross-hedge ratio the variables Degree-Day (a heating and cooling load measure) and Columbia River Flow (a capacity production output measure in hydro based electricity generation systems) (Woo et al., 2011). Accordingly, we included in the study the Multivariate ENSO Index Version 2 (MEI2) v in order to incorporate the effect of weather on hedge performance. This variable is a measurement generated by the National Oceanic and Atmospheric Administration (NOAA) to be able to quantify an assessment of ENSO in a single index. This variable is a combined Empirical Orthogonal Function (EOF) of five different variables (sea level pressure (SLP), sea surface temperature (SST), zonal and southern components of the surface wind, and outgoing longwave radiation (OLR)) over the tropical Pacific basin ((NOAA), 2019).

In the time series in which cointegration occurs, the practical interpretation of this relationship would have long and short term implications, according to Engle. Thus, to make its correct estimate, we must use an estimate based on Error Correction Model (Engle and Granger, 1987). The structure embodied in Eq. (1) would correspond to long-term behavior, while, for the short term, cointegration would lead to the short-term structure applied to the differences in the series:

$$\Delta S_t=a+\beta \Delta F_{t,T}+\sum _{i=1}^k{\gamma }_{i}log{F}_{t-i}+\sum _{j=1}^k{\delta }_{j}log{S}_{t-j}+\sum _{k=0}^k{\lambda }_k\Delta ens{o}_{t-k}+\zeta \ast e_{t-1}+{\nu }_t$$ (3)

In addition to the lagged variables to incorporate the convergence structure and price relationship, the variable $ens{o}_{t-k}$. is incorporated. The above seeks to model the climate effect of ENSO as the main driver of the short-term relationship. Lagged effects of this variable have been included, to incorporate the fact that the climate has a permanent effect on the stage of cultivation of agricultural products (Kirono and Tapper, 1999); while in the prices of electricity in Colombia this effect is maximum of one month, according to the pricing structure established for the market. The model included the logarithm of spot and futures prices, to include autoregressive process. The logarithm was taken to reflect differential processes, instead of level to level relationships. The adjustment speed, estimated by ζ, comes from taking the lagged residuals from Eq. (1). That is, these residuals correspond to $e_{t-1}=S_t-a+\beta F_{t,T}$

In the case of cointegration relationships that would have been detected from Eq. (2), we would have the following short-term relationship:

$$\Delta log{S}_t=a+\beta \Delta log{F}_{t,T}+\sum _{i=1}^k{\gamma }_i\Delta log{F}_{t-i}+\sum _{j=1}^k{\delta }_j\Delta log{S}_{t-j}+\sum _{k=0}^k{\lambda }_k\Delta ens{o}_{t-k}+\zeta \ast e_{t-1}+{\nu }_t$$ (4)

In this case, the speed of adjustment is determined with respect to the lagged residuals from estimating the relation expressed in Eq. (2), instead of Eq. (1). That is to say, $e_{t-1}=log{S}_t-a+\beta log{F}_{t,T}$. The model selected in 4 is used in our research, given that we are interested not only in hedging a level variable (price) but also in the possibilities of reducing price volatility. For this reason, difference of the logarithm is included as well as the lags of the spot and futures change. Given that ENSO is a real number, logarithm it is not possible to apply, but difference is used to state its effect on the fluctuation of spot price.

Imitating the practice developed by Adams and Gerner, the estimation in addition to being carried out by means of ECM will be chosen to use a GARCH model in order to compare the results in the estimation and to be able to find consistency in the results obtained. In this way, the estimation by means of a GARCH model (1,1) would imply that in the estimation of the model (3) and (4) the term corresponding to the error $({\nu }_t)$ had a behavior like the following:

$${\nu }_t=\sqrt{h_t^2}{u}_t,u_t\sim N(\mu ,{\sigma }^2)$$ (5)

$$h_t^2=\mu +{\theta }_1{v}_{t-1}^2+{\theta }_2\ast h_{t-1}^2$$ (6)

In sum, bibliographic review reveals that there are two precautions when making hedge-ratio estimates if the goal is to obtain a minimum variance estimator of OHR. First, one must be careful not to violate the assumptions of the OLS estimate (autocorrelation and heteroskedasticity), which is typical in financial price series. Second, in the case of nonstationary series, they should be given the appropriate treatment so that the estimates are statistically significant. Given that data reveals there are mixed-results respect to the cointegration of the spot agri-prices respect to the futures prices for different maturities (some are and some are not) different treatments are required in the estimation of MV cross- hedging ratio. All equations presented, are useful to estimate hedge ratio of stationary series. Eqs. (3) and (4) are useful to estimate just cointegrated series at first level. So the justification of the methods used in ths paper is that our goal is to estimate the OHR considering and controlling for statistical issues (as time conditioned variance, external factors as ENSO, cointegrations between markets). This research has been approved by the Comité de Ética de Investigación (Research Ethical Committee) of UNIAGRARIA considering that all information used is publicly available, gathered according to Colombian laws about information treatment, all data was aggregated for statistical purposes, no animal or human experimentation was conducted, all software and techniques used were licensed or recognized to their creators and no informed consent was required due to the econometric nature of the study and the availability of data in open and public sources.

3. Description of the data and empirical results

According to what was presented in the previous section, the information that is required for the work consists of the spot prices of the agri-prices, the prices of the electricity futures market and the quantification of ENSO (through the MEI2 measurement). The information on the first two variables, specifically concerns Colombia, while the MEI2 variable is a quantification devised by the NOAA and taken for the Pacific Basin. In the paragraphs below, we present a brief context of the sources of information that gave rise to the data collected on the variables.

First, the spot agri-prices. In 2018, Colombia's contribution to GDP in the agricultural sector is 6.3% (world average: 3.4%), which is equivalent to producing 54.6 million tons of food (0.5% of the world production) and employs 4.1 million hectares for harvest (0.03% of the world total) (Bank, 2019). Small farmers are responsible for 90% of agricultural production (Guarín, 2013). Due to resource constraints and the large separation between cultivation areas and consumption centers, producers sell their production to intermediaries; who may sell to other intermediaries. In some cases, there are more than three intermediaries before the product arrives to end-consumer or a Farmer's Market. The principal marketplace of this type is called CORABASTOS. This the foremost stockpiler and agri-market, which trades 12.400 ton of agri-products from all the country. Spot agri-prices were taken from its online price data base (CORABASTOS).

Accordingly, the spot prices for this study come from one of the largest collection centers in Colombia. The data series include information for 88 different agricultural products, taken from March 31, 2003 to May 31, 2019. Due to shortcomings in the source of origin, the series do not have the consecutive price information for the entire time window indicated. However, since January 2009 there is a complete sequence of these time series. The information is collected monthly. Foods are grouped according to three categories: Vegetables, Fruits, and Tubers. In Appendix A you can find the detail of the agricultural products included in the study, as well as the statistical characterization of the time series.

As for the futures prices of electric energy, these prices are formed daily in the market, in the same rounds of negotiation of the spot price. The price setting is subject to a sealed-bid auction mechanism where 44 generators and 85 electricity traders converge. Contract prices are published at the end of the daily negotiation round for all negotiated contracts. The negotiated contracts are of two types, they are identical in all characteristics, except in the negotiated amount of the underlying asset (amount of energy). The largest contract trades 360,000 kWh, while the smallest 10,000 kWh. The settlement of the contracts is financial, mediated by a clearing house, and takes place two business days after the end of the month. The contracts traded are only for maturity at the end of each month for which they are negotiated. As the market for electricity price derivatives began since October 2010, the information is available from that date on a monthly basis. Although the information is in daily periodicities, we have taken the price at the end of each month because the data series of the agri-prices have this periodicity. Contracts with maturity up to 6 months were considered. In Appendix B it is possible to find the detail of the technical characteristics of each contract. Appendix C contains the statistical characterization of the contract price data series.

As for MEI2, the quantification of this index is a process carried out by the NOAA. This index combines oceanic and atmospheric variables. The index can take positive values (indicating favorable conditions for the occurrence of ENSO) or negative values (indicating the occurrence of “La Niña”, the cold phase of ENSO). When the index exceeds the threshold of +/0.5, an occurrence of the phenomenon is declared (be it El Niño or La Niña of ENSO). This index is officially used by NOAA since 2019 to carry out the follow-up and official press releases. Version 1 of this index was valid until 2018, however, due to methodology update it was changed, for precision purposes. Information on this index is reported from 1979 to today. The information related to this index is reported monthly. In Appendix C, we carry out the statistical characterization of the time series.

Now, after the series of data used for the study have been described, we present the results found below. When characterizing stationarity, 67 stationary series and 23 non-stationary series were found. This process was carried out using the Phillips-Perron test (Peter and Perron, 1988), in two modalities; including a constant and including constant and time trend. The 67 stationary series correspond to those in which the null hypothesis was not verified. Of the 23 non-stationary series, 11 rejected the null hypothesis in both versions of the test, which verified its non-stationary character. The remaining 12 series generated contrary results. Each one rejected null hypothesis when the test was performed with only constant, but it was not rejected when performing the test with time trend. Consequently, we classified them as non-stationary, since incorrectly classifying them as stationary would lead to unreliable estimates of the model used. Both previous and subsequent results have been evaluated with a statistical significance of 5% of lower.

This preliminary findings about the stationarity of the spot prices is important for planning and agrarian policy in Colombia. No previous study has stated this condition over colombian agricultural commodities. Its importance relies on the fact that, as mentioned, Colombian government invest more than 92% of agro-subsidies in ex post hedging (to overcome loses from price fluctuation, natural phenomena, among others). The stationarity of the price of 67 agri-products could lead to policymakers and agricultural authorities to provide technical assistance in planning suitable seasons to plant. Also, some level of coordination between farmers associations could be stated to leverage the effects of this stationarity, in the form of sequential sowing, crops rota, or diversification through farming of different products. Technical assistance could lead to release some resources form ex-post intervention to planning ahead assistance.

On the side of non-stationary series, its characterization it is also important from the perspective of structural changes. The portrayal of non-stationary price in agri-products is important because it could be used as tool to give priority to these products in two senses. The first one, to study the underlying phenomena that leads to this non-stationarity; for example, Climate change have been documented as a permanent source of variation in prices, crop yields and demand of some assets (Poveda and Álvarez, 2012; Zhiwei et al., 2018). On the other hand, the non-stationarity effect could be a subject of study due to its implications in policy and regulations; in housing prices, the non-stationarity prices of some household developments have led to some questions about sustainable development of those markets (Cai and Magazzino, 2019; Mou et al., 2017). In the case of agri-products, speculation and arbitrage from intermediate brokers are elements to study, due to their impact to the sustainability of the colombian agricultural market.

After the previous characterization and in line with the literature, we proceeded to estimate between the dependent variables (agri-prices) and the independent variables (prices of futures contracts) the existence of a cointegration relationship for the non-stationary series. This test is performed by evaluating whether the residuals in Eq. (1) for the non-stationary series are stationary, which would mean the existence of cointegration (Engle and Granger, 1987). Table 1 shows the results of this evaluation. We discarded those series that did not pass the tests, since their behavior does not conform to the proposed methodology and therefore the estimates made would not be significant. Those significant at 10% will be carefully observed to inspect the possible effects of a misclassification by the unit root test.

Table 1.

Estimation of cointegrated series. In ∗ and ∗∗ those in which the null hypothesis is rejected in the Phillips-Perron test are indicated. FE [T] corresponds to the futures contract with maturity within T months.

Type of product	Agri-product1	FE0	FE1	FE2	FE3	FE4	MEI2
Fruit	Banano criollo (A banana variety)	∗	∗	∗	∗	∗	∗
	Lulo (Quito orange)	∗	∗	∗	∗	∗	∗
	Naranja grey (An orange variety)	∗	∗	∗	∗	∗	∗
	Tomate de arbol (Solanum betaceum)						∗∗
Vegetable	Pepino (Cucumber)						∗
	Pepino comun (A cucumber variety)	∗	∗	∗	∗	∗	∗
	Berenjena (Eggplant)	∗∗	∗∗			∗∗
	Haba verde sabanera (A broad bean variety)	∗	∗	∗	∗	∗	∗
	Pimenton (A pepper variety)	∗∗	∗∗		∗∗	∗∗	∗∗
	Cebolla cabezona roja (An onion variety)	∗	∗	∗	∗	∗	∗
Tuber	Papa r12 industrial (A potato variety)	∗	∗	∗	∗	∗	∗
	Papa r12 roja (A potato variety)	∗	∗	∗	∗	∗	∗
	Papa r12 negra (A potato variety)	∗	∗	∗	∗	∗	∗
	Yuca armenia (A yucca variety)	∗	∗	∗	∗	∗	∗
	Yuca llanera (A yucca variety)	∗	∗	∗	∗	∗	∗

¹∗ statistically significant at 5% - ∗∗statistically significant at 10%. In parenthesis English description of product.

Regarding the implications of this cointegrated variables, this finding it is important because it could be used by market makers in at least three ways. The first one, it is to offer assets in the financial market to reduces the volatility of their portfolios, as has been proved in other markets (Ausloos et al., 2020). The other one, it is a relation that could be employed to generate financial inclusion to Colombian farmers. Given that Colombia is a developing country, it is highly desirable to link this two markets (financial and agricultural), as they have found to be a strong predictor of industrialization in the long run (Adeleye et al., 2020). Finally, as has been documented in other products as raw milk, this relationship could be used to study the effects of regulation/desregulation and international trade agreements on prices of agricultural products (Fotis & Polemis, 2020).

Back to the estimation of the OHR, the models were estimated according to the equations described in the previous section. The estimates were made in such a way that for each agri-product considered, a model was estimated with each of the contracts, to evaluate the feasibility of making a cross-hedge at different horizons. In the first instance, the model described in Eq. (1) was estimated to corroborate the correspondence with the literature. In fact, for all products it was found that the estimated models are not statistically significant (mainly due to the correlation of residuals), except for one, a variety of tomato called "Tomato chonto".

For this product, we found a relationship that lacks problems or transgressions to the OLS assumptions. The ratio has a hedge efficiency (measured by R2) of between 15.89% and 17.38%. Regressions Log-likelihood ranges between -617.46 and -615.78. Accordingly, we reformulated the model adding as a regressor the variable related to ENSO (MEI2) along with its lags up to 6 periods. This addition improves R2 (between 19.69% and 23.45%) on average by 6.39% as well as Log-likelihood (between -614.64 and -612.73). The additional regressor was added in terms of first difference rather than level for MEI2, hypothesizing that a change in MEI2 alters the levels of the variable, and not its level. The cross-hedge for different moments was significant in all the models, and a reduction in the efficiency is not observed according to the horizon of hedge; whereas if an increase in the size of the position is observed as the time increases, contracts that mature the same month have ratios of 1.37, while 6-month contracts have ratios of 4.92 (they are ratios with respect to the price level). The sign of the variable associated with ENSO is shown with a negative sign for all types of contract.

According to described in th literature review section, the model described in Eq. (1) was adjusted to include the lags of the regressors, seeking to take into account the price convergence effects described in the previous section. When making this modification, 13 products were found to have statistically significant models with R2 between 0.51 and 0.87 (Log-likelihood ranges between -682.7 to -459.6). See Appendix D for more detailed results. By repeating the above procedures using the model embodied in Eq. (2), the results are similar; the product “Tomato chonto” has a relationship, but only with the 6-month contract with an R2 of 23.98% and Log-likelihood -26.75. When estimating the model considering the lags of the regressor variables, only 6 products generate statistically significant results. None coincide with the estimates for the analogous procedure with Eq. (1). The main estimates are presented in Appendix E.

Now, for the products to which a cointegration relationship was identified, Eqs. (3) and (4) were estimated, using the ECM. From relationship 4, no statistically significant estimate was obtained. While, from Eq. (3), the only product that produced a statistically consistent estimate was “Yucca llanera” with the six-month contracts. For this estimate –in variable levels-, it was estimated that the long-term relationship generates a coefficient of 3.61, while the short-term relationship –estimated in differences- generates a hedge ratio of 1.24, a term associated with the ECM of -0.077. Likewise, it is necessary to remember that some terms associated with ENSO were included. For this model, we found significance for terms associated with the value of the variable in the period, as well as lags at 2, 3 and 5 months (with positive coefficients of 0.04, 0.07 and 0.09 respectively). The R2 obtained is 0.412 while the log-likelihood corresponds to -474.36. So far, as it is possible to show, the models obtained have low levels of efficiency, measured from R2 and log-likelihood perspective. Although the models presented have passed the corresponding autocorrelation and heteroskedasticity tests, the p-values have been close to the rejection zone.

Considering that there were series that were classified as stationary, the cross-hedge ratio was estimated for these using Eqs. (3) and (4), using a GARCH estimate (1,1) (Eqs. (5) and (6)) and excluding the term alluding to the ECM (as they are not cointegrated, it is not required). The results obtained are presented below in Tables 2 and 3:

Table 2.

Statistically significant relationships for estimation of Eq. (3) with no ECM term.

Agri-product	Contract maturity	Beta 1 – Hedge ratio	Beta 5 - ENSO	Beta 6 - ENSO(-1)	Beta 8 - ENSO(-3)	R2	Log-likelihood
Papa criolla lavada (A potato variety)	FE2	0.972	264.962	-374.963		0.535	-585.81
Papa criolla lavada (A potato variety)	FE1	1.112	239.935	-364.748		0.531	-586.06
Lulo (Quito orange)	FE1	1.202			280.6814	0.744	-593.28
Mango tommy (A mango variety)	FE6	7.091	-133.910			0.542	-649.74
Breva (Fig)	FE5	8.836				0.478	-661.51
Breva (Fig)	FE4	6.661		-699.843		0.461	-662.82
Breva (Fig)	FE3	5.480		-699.344		0.450	-663.26

Table 3.

Statistically significant relationships for estimation of Eq. (4) with no ECM term.

Agri-Product	Contract Maturity	Beta 1 – Hedge Ratio	Beta 7 - ENSO(-2)	Beta 8 - ENSO(-3)	R2	Log-likelihood
Mazorca (Ear of corn)	FE2	0.158	-0.120	0.270	0.46	-14.61
Papa criolla lavada (A potato variety)	FE1	0.179	0.000	0.042	0.50	5.90
Papa criolla lavada (A potato variety)	FE5	0.173	0.105	0.036	0.47	6.30
Curuba boyacence (A variety of passiflora tarminiana)	FE6	0.252	-0.221	0.069	0.49	29.97
Limon tahiti (A variety of lemmon)	FE5	0.326	0.040	-0.005	0.48	-9.52
Limon tahiti (A variety of lemmon)	FE6	0.425	0.035	0.007	0.49	-7.90
Mango chancleto (A mango variety)	FE5	0.271	-0.137	0.122	0.30	-23.22
Mango chancleto (A mango variety)	FE6	0.317	-0.143	0.128	0.30	-23.28
Mango tommy (A mango variety)	FE4	0.298	-0.231	0.261	0.58	-23.55
Naranja ombligona (An orange variety)	FE2	0.123	-0.102	0.005	0.27	43.41
Naranja valencia (An orange variety)	FE2	0.135	-0.054	-0.065	0.32	43.55
Auyama (A pumpkin variety)	FE3	0.139	-0.027	0.151	0.61	54.65
Auyama (A pumpkin variety)	FE4	0.144	-0.018	0.145	0.62	55.17
Auyama (A pumpkin variety)	FE5	0.157	-0.023	0.144	0.63	55.80
Auyama (A pumpkin variety)	FE6	0.161	-0.068	0.127	0.61	60.26

The results showed in Tables 2 and 3 are of highly interest because they are the first statistical approach in Colombia to this kind of hedging. Even though the R2 are not the highest found in literacy, this statistical significance is encouraging for the goal of this research. It is important to highlight that the prices obtained are aggregated published by the biggest agricultural wholesaler in Colombia. Also, it is highly important to consider that the variable accounted for the ENSO climate fluctuation it is a general estimation for the whole Pacific Coast, and not for the specific regions of production in Colombia. In spite of this limitations, these results open the door to a financial market integration to use existent financial futures market to hedge at least the production of the agri-products referred in Tables 2 and 3. The implications of this findings its that regulatory bodies can explore and enhance efforts to refine data (for example, employ daily data, or specific region/product data) and state policies oriented to replace subsidies with technical assistance and financial education to use electricity futures market to hedge agri-price risks.

Results of Tables 2 and 3 were tested for a robustness check considering structural changes in the way they were estimated. To account for this change, Structural Vector Autoregressive (SVAR), Threshold GARCH (TGARCH) and Exponential GARCH (EGARCH) were used to re-estimate the OHR. Results obtained from these procedures are summarized in Tables 4 and 5.

Table 4.

Robustness check to estimations of Table 2. Blank spaces are non-statistically significant relationships.

Agri-product	Contract maturity	SVAR	TGARCH	EGARCH
Papa criolla lavada (A potato variety)	FE2			0.71∗
Papa criolla lavada (A potato variety)	FE1	0.95∗∗		1.13∗∗
Lulo (Quito orange)	FE1
Mango tommy (A mango variety)	FE6
Breva (Fig)	FE5	6.65∗∗
Breva (Fig)	FE4	6.49∗∗	3.91∗
Breva (Fig)	FE3		3.94∗∗	7.09∗∗∗

∗ statistically significant at 5% - ∗∗statistically significant at 10%. In parenthesis English description of product.

Table 5.

Robustness check to estimations of Table 3. Blank spaces are non-statistically significant relationships. ∗ statistically significant at 5% - ∗∗statistically significant at 10%. In parenthesis English description of product.

Agri-Product	Contract Maturity	SVAR	TGARCH	EGARCH
Mazorca (Ear of corn)	FE2	-0.3619∗∗	-0.3428
Papa criolla lavada (A potato variety)	FE1
Papa criolla lavada (A potato variety)	FE5
Curuba boyacence (A variety of passiflora tarminiana)	FE6	0.2561∗	0.3017∗	0.3433∗
Limon tahiti (A variety of lemmon)	FE5
Limon tahiti (A variety of lemmon)	FE6			0.3645∗∗
Mango chancleto (A mango variety)	FE5	0.416∗∗
Mango chancleto (A mango variety)	FE6	0.523∗∗
Mango tommy (A mango variety)	FE4
Naranja ombligona (An orange variety)	FE2
Naranja valencia (An orange variety)	FE2
Auyama (A pumpkin variety)	FE3	0.262∗∗∗	0.2686∗∗	0.1405∗∗
Auyama (A pumpkin variety)	FE4	0.286∗∗∗	0.1770∗∗∗	0.218∗∗
Auyama (A pumpkin variety)	FE5	0.1944∗∗		0.2049∗∗
Auyama (A pumpkin variety)	FE6	0.1694∗∗	0.1381∗	0.2717∗∗∗

From the results of Tables 5 and 7, there are various highlights. The first one is that only two products kept the statistical significance of the estimated OHR between the different estimation methods used. Auyama (a pumpkin variety) showed a stable relation with future contacts with maturities of 3–6 months. Also, Curuba boyacense (A variety of passiflora tarminiana) exhibited a hedging relation with contracts to six-months. Statistically speaking, the TGARCH and EGARCH revealed for these two products that there are not asymmetrical shocks (due to good or bad news). Authors consider that his fact was, statistically speaking, the reason that led to statistically significance and similar estimations of the OHR. From the farmer point of view, the hedging relationship could be stated to the fact that this two crops have similar harvest times (3–4 months), are cropped in similar environmental conditions (altitude, precipitation, tropical weather) and technical and physically required the same techniques to be cultivated (both are vine). About their relationship to the electricity market, researchers hypothesize that the fact that extreme events (as excessive rains or drought climate) have short-time consequences in almost the same span (two to four months).

Table 7.

Estimate of the performance of the hedge ratio estimated in Table 3.¹

	FE1	FE2	FE3	FE4	FE5	FE6
Mazorca (Ear of corn)		-26.69%, 7%
Papa criolla lavada (A potato variety)	-52.1%, 6%				3.94%, 11%
Curuba boyacence (A variety of passiflora tarminiana)						-22.92%, -32%
Limon tahiti (A variety of lemmon)					48.64%, -14%	-1095.39%, 23%
Mango chancleto (A mango variety)					109.03%, -6%	-41.14%, -14%
Mango tommy (A mango variety)				9.42%, -1%
Naranja ombligona (An orange variety)		-36.45%, 18%
Naranja valencia (An orange variety)		-40.01%, 21%
Auyama (A pumpkin variety)			-112.55%, -9%	-20.04%, -19%	-24.22%, -25%	-19.27%, 11%

¹¹ ∗ % of change in the average profit loss, after comma % of change on Std. Dev. of P&L series.

The products that showed at least a statistically significant relationship with the SVAR, GARCH or EGARCH could be a highlight regarding the relationships not modelled. In this study, the hedging relationship was controlled only to an exogen variable: the ENSO. Other variables as supply and demand of each product, regional effects (local shocks), substitute goods and services (i.e. some fruits are bought when others are highly prices) could be important relationships missed in the model. For example, the Fig showed a OHR significant under the SVAR, but non-significant to GARCH and EGARH. This could be stated since the exogen variable ENSO revealed a permanent shock (a long-lasting drought or rain season) instead punctual shocks in volatility (bad news – good news approach of EGARCH model). Another example could be the inner relationship that SVAR states within the spot and future prices, as well as the augmented impact of ENSO over both prices. So, in this case, estimation of a OHR need to consider more specific information about the assets to be hedged, in order to achieve more robust estimations.

In Table 4, the estimation for Lulo and Mango Tommy, showed that none of techniques used stated an OHR. In this case, researcher consider that these two products could be a type II error manifestation. That is, despite the stationarity of the series was tested, both series could be non-stationary and in consequence, need ad different treatment. Also, the quality of information for these two series could be improved in order to prove if the product could be cross hedged. So, for these two series a OHR could not be stated.

Finally, from the results of Tables 2 and 3, we proceeded to perform a back-testing analysis. For this analysis, the series of price data was used from May 2017 to May 2019, which were not included in the estimation of the models and were separated precisely for this purpose. The objective of this procedure is to evaluate the performance of the models under realistic situations. Although the R2 and log-likelihood showed low theoretical performances, in line with the objective of the study, it is desired to conclude whether there is a feasibility of using the proposed hedges as an element to mitigate risk and stabilize farmers' cash flows. The uncovered profit and loss series (P&LUn) is simply calculated as the percentage of change between the spot price t months ahead, according to the hedge horizon, and the current month price for the agri-product. The series for a hedged position under the models presented in this section (P&Lhed) is calculated as: i) the change between the spot price of electricity in t months and the price of the futures contract in the month, ii) the result of i) is weighted by the hedge ratio and, iii) is added to a weighting prior to P&Lun. Next, in Tables 6 and 7, we presented the performance evaluated under the models proposed in Tables 3 and 4 respectively. Performance is measured under two criteria. The first, the% change in the P&L function in a covered scenario vs. an uncovered one. And the second criterion corresponds to the percentage change in the standard deviation of the covered series vs. the uncovered series.

Table 6.

Estimate of the performance of the hedge ratio estimated in Table 2.¹

	FE1	FE2	FE3	FE4	FE5	FE6
Papa criolla lavada (A potato variety)	-323.68%, 65%	-72.56%, 69%
Lulo (Quito orange)	-2584.18%, 138%
Mango tommy (A mango variety)						-472.19%, 922%
Breva (Fig)			31059.23%, 760%	2300.55%, 1634%	22260.32%, 1761%

¹∗ % of change in the average profit/loss, after comma % of change on Std. Dev. of P&L series.

4. Discussion and conclusions

This study investigates the feasibility of associating two markets from different economic sectors, linked by an external variable that heavily influences the behavior of their prices. Four different models were used to address the problem: using OLS levels, logarithm and difference models, ECM models (when cointegration exists), and GARCH process to model time dependent volatility. The inclusion of differences over spot and future prices, as well as the logarithm of levels was introduced to model influence not only the level but also in the reduction of volatility of the agri-prices- Of these models, the most recent literature indicates the appropriacy of the last two, as compared to the first two, for effects of avoiding spurious relationships (Adams and Gerner, 2012; Engle, 1982). Moreover, in an effort to incorporate the variable that is hypothesized to link the two markets, a variable associated with ENSO occurrence, a very relevant climatic event for both markets, was incorporated into the hedge ratio estimation model (Woo et al., 2011). As the electricity derivative market has permanent derivatives futures contracts with multiple hedging horizons, the models proposed herein aimed to identify the most appropriate vehicle to carry out financial cross-hedging.

The first finding of note is that there was no preponderance regarding the instrument to be used for cross-hedging. All contracts, which provided horizons of between one to six months, presented statistically significant estimations for cross-hedging purposes. The practical implications of this finding is that there is a prevalent relationship to be student in order to link the electricity market to cross hedge agri-product. This is relevant from the perspective of field out of the scope of this study, as for example financial inclusion or climate smart agriculture. Almost the opposite occurred with agri-prices, for which not all products exhibit a feasibility to cross-hedging. On contrast of the results, observe that products with enhanced performance in the model estimation are cultivated in the sectors which ENSO affects most heavily, in Colombia.

The variable associated with ENSO causes representative effects when observed separately. Similarly, time lags were found to be significant for products in differing climatic conditions. The signs thereof depended on the type of agri-product. Products which required climatic characteristics typical of cold climate areas possessed positive signs, with respect to the MEI2 index, while their lags were negative. It should be considered that the measurements taken for the ENSO estimation were taken from an international reference that includes the entirety of the pacific basin. As such, reconsidering the use of a more specific indicator may be useful for modeling and cross-hedging purposes. Similarly, the importance of geographical location should be considered together with the possibility of hedging establishment, as well as the climate and spatial location interdependence. Indices specific to Colombia, or indices created specifically for Colombia should be contemplated, in order to better model cross-hedging performance (Conradt et al., 2015; Isakson, 2015b). This index, in the case of agri-products, must consider the accumulated effects of the climate, considering that the performance crops exposed, during their phenological period, to variability in climatic conditions, together with effects associated with supply and demand, may see their prices affected.

The results, generally, do not support the feasibility of using the Colombian electric derivative market. Estimations performed with the different methodologies reflect inconveniences in the estimated coefficients, and do not reflect performances that would comply with the objective of risk mitigation. Table 6 shows the way in which estimated relationships fail to minimize risk for farmers. The only method which may be considered appropriate is estimation by way of models which consider volatility over time. For these estimations, it was observed that hedge ratios were estimated for nine agri-products which reduced risk exposure. Despite this statistical significance, there are not a high risk mitigation; it was found that risk reductions accounts for only 32% in the best case and averaged -10.72% for all the models evaluated. A robustness check showed that models used to estimate OHR rely on assumptions too strong (ENSO variable as a weather indicator or the one way relationship (futures to spot price), for example). Taking in account this robustness analysis, it was found that OHR estimated for two products is significant and relevant.

Due to the exploratory nature of this research and the shortage of previous studies, the findings described above are important for at least two reasons. The first one, it is important for developing countries to start to collecting data relevant to national issues. In the Colombian case, there are a huge lack of information regarding agri-prices. Our study compiled and unprecedent time series of agri-prices and analyze it to explore a relief strategy. Also, the rigorous information to develop, measure and tracking climate change impacts is unavailable or kept in private. In our case, a global, non-colombian index was used to model the climate effect.

The Second reason, is a paradoxical situation; countries like Colombia are called to supply and support global food security in order to achieve SDGs. In contrast, migration, poverty and climate change are forcing migration to cities reducing agricultural labor, traditional knowledge about farming and farming activity. Our study contributes to explore practical mechanisms with existing markets to relieve those phenomena while deep solutions are employed.

Future research should focus on three principal elements: firstly, the use of data regarding the price paid to producers. The present study used wholesaler prices, and as such, effects including intermediary and transport costs distorted producer prices. Further, it is the producer who is truly interested in cross-hedging, as the merchant has the option of refusing to purchase agri-products when there is no demand, while farmers do not have the option of not to sell, owing to the perishable nature of their goods. While our study proved the infeasibility of current market conditions to hedge, it is also important to evaluate other cross-hedging strategies. For example, time variant OHR, conditioned hedge ratio to geographical, or product are also important to research. This could provide base of pyramid populations with cost-effective support to farming activities.

Secondly, a greater effort should be made to consider more specific data series. Herein, monthly relationships were explored, owing to two elements: the liquidation of future contracts was performed monthly, and the index for ENSO quantification occurred monthly. Thus, efforts to create weekly or daily models may yield improved results. The need for climate index are also addressed. The information about weather influence is poorly reflected in our models due to its lack in Colombia. It is required that research institution and government authorities improve the availability as well as the quality of this kind of information. In Colombia, there are not public climatic indexes that describe regional weather and climatic evolution.

Thirdly, nine products were identified which, together with GARCH process estimation, created reduced risk. In this quantification, linear effects were assumed. However, non-linear effects may also be examined, as may their impact on the determination of hedge ratios and the estimation of seasonal hedge ratios (Woo et al., 2011).

Declarations

Author contribution statement

G. Barrera: Conceived and designed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

A. Cañón: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Wrote the paper.

J.C. Sanchez: Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

This work was supported by Fundacion Universitaria Agraria de Colombia UNIAGRARIA and Universidad EAN.

Data availability statement

Data will be made available on request.

Declaration of interests statement

The authors declare no conflict of interest.

Additional information

No additional information is available for this paper.

Appendix A.

Table A1.

Statistical characterization of the variables used as dependent variables (CORABASTOS).

Type of agri-product	English denomination	Mean	Median	Maximum	Minimum	Std. Dev.	Skewness	Kurtosis	Jarque-Bera P-value
Fruit	Avocado	16157.5	2800	200000	1800	44498.7	3.1	10.7	0.0
Fruit	A banana variety	1251.7	1067	2000	933	322.4	1.1	2.8	0.0
Fruit	A banana variety	900.0	875	2000	700	194.9	2.6	14.1	0.0
Fruit	A grape variety	3002.0	2920	4800	1760	631.5	0.6	3.7	0.0
Fruit	Cantaloupe	1877.5	1700	13000	1000	1327.6	7.5	63.2	0.0
Fruit	Coconut	10028.2	9167	15000	3000	2482.8	-0.2	3.0	0.8
Fruit	A variety of passiflora tarminiana	1501.3	1500	2500	900	423.2	0.6	2.8	0.1
Fruit	A variety of passiflora tarminiana	1318.7	1273	2273	682	353.0	0.6	2.7	0.1
Fruit	Feijoa	4545.8	4500	8000	2500	1134.8	0.7	3.4	0.0
Fruit	Fig	5650.0	5000	10000	3000	1533.2	0.7	2.6	0.0
Fruit	Guava	2718.8	1500	20000	1000	3677.6	3.3	12.5	0.0
Fruit	A variety of lemmon	1263.4	1143	3286	714	461.5	1.7	6.9	0.0
Fruit	A variety of lemmon	1611.3	1429	4000	714	707.6	1.2	3.9	0.0
Fruit	Quito orange	2355.8	2400	4800	88	909.4	-0.4	4.4	0.0
Fruit	A mango variety	1106.8	909	2727	455	493.9	1.2	4.5	0.0
Fruit	A mango variety	1444.3	1364	4545	636	721.6	1.8	7.1	0.0
Fruit	A mango variety	2102.3	1818	6818	727	1312.7	1.6	5.8	0.0
Fruit	Blackberry	2174.8	2143	4286	214	806.7	-0.7	4.1	0.0
Fruit	Apple	3232.5	3000	5000	2300	525.7	1.0	3.9	0.0
Fruit	An orange variety	951.0	1000	1600	560	189.6	0.7	4.4	0.0
Fruit	A variety of tangerine	1856.3	1800	4000	800	714.7	0.6	3.1	0.1
Fruit	An orange variety	803.3	800	1500	460	194.9	0.7	4.6	0.0
Fruit	An orange variety	1272.5	1000	2200	700	494.3	0.6	1.6	0.0
Fruit	An orange variety	955.3	1000	1600	560	186.6	0.5	4.1	0.0
Fruit	A papaya variety	1179.4	1250	1727	45	383.0	-1.7	6.0	0.0
Fruit	A papaya variety	1121.5	1100	2000	750	248.8	0.6	3.7	0.0
Fruit	A papaya variety	862.0	840	1520	560	167.5	1.1	5.0	0.0
Fruit	A papaya variety	979.4	1000	1800	600	205.7	1.2	5.4	0.0
Fruit	Passiflora ligularis	3141.1	2857	6429	1000	1106.5	0.8	3.6	0.0
Fruit	Passiflora edulis	2046.9	2000	5000	100	859.7	-0.1	4.6	0.0
Fruit	Watermelon	774.4	750	1500	450	196.3	0.9	4.1	0.0
Fruit	A pineapple variety	668.9	688	938	313	107.7	-0.3	3.5	0.3
Fruit	Hylocereus undatus	6672.5	6000	17000	2500	3385.5	1.1	3.6	0.0
Fruit	A grape variety	3106.0	3200	4800	1760	662.2	0.3	3.1	0.6
Fruit	Soursop	3039.4	2800	25000	2000	2514.0	8.5	74.6	0.0
Fruit	Strawberry	4478.8	4400	6000	3000	553.9	0.6	3.5	0.1
Fruit	Solanum betaceum	1603.0	1800	2400	40	607.5	-1.1	3.9	0.0
Fruit	A variety of tangerine	1843.2	1591	3864	773	755.1	0.8	3.2	0.0
Fruit	A grape variety	2958.0	2800	4800	1760	651.4	0.7	3.5	0.0
Vegetable	Artichoke	3080.0	3000	6000	1200	1060.5	0.5	3.0	0.2
Vegetable	A French bean variety	2023.8	1900	4000	600	715.2	0.5	2.7	0.2
Vegetable	Beet	776.3	600	3000	240	466.8	2.0	8.5	0.0
Vegetable	Broccoli	1994.8	1667	6667	417	1352.6	1.5	4.9	0.0
Vegetable	Cabbage	677.8	600	2000	200	378.4	1.6	5.7	0.0
Vegetable	Carrot	1327.0	1000	4000	500	681.8	1.8	6.8	0.0
Vegetable	Cauliflower	1348.8	1200	4000	500	755.2	1.9	6.8	0.0
Vegetable	Celery	721.9	600	2000	300	393.4	1.5	4.9	0.0
Vegetable	Chard	536.3	500	1500	200	248.2	1.4	5.8	0.0
Vegetable	Ear of corn	1011.3	950	2400	400	446.4	1.1	4.0	0.0
Vegetable	Coriander	1806.3	1500	8000	300	1368.8	1.8	7.6	0.0
Vegetable	Cucumber	1988.8	1500	12000	700	2183.4	3.5	14.7	0.0
Vegetable	A cucumber variety	1956.3	1500	8000	700	1531.9	2.9	11.3	0.0
Vegetable	Eggplant	3035.0	1600	16000	1000	4044.3	2.7	8.6	0.0
Vegetable	Garlic	6247.5	6000	13000	4000	1926.6	1.5	5.3	0.0
Vegetable	A bean variety	2042.5	2000	3800	1000	621.7	0.9	3.6	0.0
Vegetable	A bean variety	2232.5	2200	4000	1200	623.9	0.9	3.6	0.0
Vegetable	A broad bean variety	1435.0	1200	4800	800	669.2	2.9	12.9	0.0
Vegetable	Green pea	3183.8	3000	8400	1600	1295.9	1.6	6.1	0.0
Vegetable	Lettuce	907.5	800	2000	400	341.5	1.1	4.0	0.0
Vegetable	A pepper variety	3118.8	2500	13000	1200	2323.7	3.3	12.9	0.0
Vegetable	A pumpkin variety	891.3	800	1800	600	225.0	2.1	8.7	0.0
Vegetable	A pumpkin variety	11087.5	10000	30000	1000	6109.1	1.4	4.8	0.0
Vegetable	Radish	11470.8	10000	30000	1333	6119.0	1.0	3.8	0.0
Vegetable	An onion variety	1630.0	1650	3400	600	612.4	0.6	2.7	0.1
Vegetable	Scallion	2600.0	2300	7200	1000	1308.2	1.6	5.7	0.0
Vegetable	Spinach	1432.5	850	20000	400	2320.6	6.7	52.8	0.0
Vegetable	A tomato variety	1526.2	1364	2955	545	590.0	0.7	2.7	0.0
Vegetable	A tomato variety	1561.2	1455	3182	545	669.0	0.7	2.7	0.0
Vegetable	A tomato variety	1973.3	1591	22727	545	2434.1	7.9	67.8	0.0
Vegetable	A zucchini variety	10812.5	10000	30000	1500	4569.7	1.0	5.8	0.0
Tuber	Arracacha	1687.5	1300	5000	700	1032.7	1.7	5.0	0.0
Tuber	A potato variety	1383.8	1200	4200	600	664.6	2.0	8.0	0.0
Tuber	A potato variety	1703.8	1600	4400	800	698.5	1.9	7.1	0.0
Tuber	A potato variety	906.8	760	2100	400	407.0	1.2	3.6	0.0
Tuber	A potato variety	964.1	880	1900	480	360.0	0.9	2.9	0.0
Tuber	A potato variety	706.5	580	1600	300	331.8	1.0	3.0	0.0
Tuber	A potato variety	1435.4	1400	4000	800	517.9	2.0	9.7	0.0
Tuber	A potato variety	1282.8	1200	3600	700	455.8	2.1	10.4	0.0
Tuber	A potato variety	801.5	680	1700	360	350.7	1.0	2.9	0.0
Tuber	A yucca variety	1080.0	1000	2000	600	351.4	0.8	2.6	0.0
Tuber	A yucca variety	1015.4	966.5	2000	600	313.1	1.0	3.4	0.0

Appendix B.

Table A2.

Characteristics of futures contract offered on electricity futures market(DERIVEX, 2019).

Contrato Futuro de Electricidad Mensual (ELM)
Activo Subyacente	Precio de electricidad (24 horas)
Tamaño del contrato	360.000 kWh
Generación de contratos	Mensual
Tick de precio	0.05 pesos por kilovatio hora
Método de liquidación	Liquidación financiera
Último día de negociación	Último día hábil del mes de entrega
Día de vencimiento	Segundo día hábil del mes siguiente al mes de entrega
Precio de liquidación	Promedio aritmético de los precios de referencia del subyacente de cada uno de los días del mes
Parámetros de cantidad para la Celebración y Registro	Cantidad máxima para ingresar una orden: 2000 contratos. Se podrá solicitar el registro de operaciones por una cantidad mínima de un (1) contrato
Parámetro de barrido	1000 ticks

Table A3.

Characteristics of smaller futures contract offered on electricity futures market(DERIVEX, 2019).

Contrato Mini de Futuro de Electricidad Mensual (ELS)
Activo Subyacente	Precio de electricidad (24 horas)
Tamaño del contrato	10.000 kWh
Generación de contratos	Mensual
Tick de precio	0,05 pesos por kilovatio hora
Método de liquidación	Liquidación financiera
Último día de negociación	Último día hábil del mes de entrega
Día de vencimiento	Segundo día hábil del mes siguiente al mes de entrega
Precio de liquidación	Promedio aritmético de los precios de referencia del subyacente de cada uno de los días del mes
Parámetros de cantidad para la Celebración y Registro	Cantidad máxima para ingresar una orden: 72.000 contratos. Se podrá solicitar el registro de operaciones por una cantidad mínima de un (1) contrato
Parámetro de barrido	1000 ticks

Appendix C.

Table A4.

Statistical characterization of futures contracts.

Name	Variable abbreviation	Mean	Median	Max.	Min.	Std. Dev.	Skewness	Kurtosis	Jarque-Bera P-value
Current month Foward price	FE0	191,93	163,50	1114,89	45	157,51	3,67	19,32	0
1-month ahead foward	FE1	190,61	167,20	810	88	118,41	3,72	17,96	0
2-month ahead foward	FE2	186,21	166,55	782,11	94	110,13	3,81	18,61	0
3-month ahead foward	FE3	185,15	167,89	761,29	100	103,88	3,85	19,26	0
4-month ahead foward	FE4	178,84	168,09	686,84	98,31	88,63	3,78	19,46	0
5-month ahead foward	FE5	172,44	165,91	572,19	93,14	69,14	3,84	21,70	0
6-month ahead foward	FE6	166,47	165,23	450	92,57	47,98	2,57	16,44	0
Multivariate ENSO Index Version 2 (MEI.v2)	MEI2	-0,03	-0,25	2,21	-1,37	0,88	1,14	3,55	,104

Appendix D.

Table A5.

Hedge ratio estimated with Eq. (1) and regressors lagged variables.

Agri-product/Contract	FE0	FE1	FE3	FE4	FE5	FE6
Papa r12 roja (A potato variety)	0,271 [0,84;-504,46]					0,56 [0,87;-459,66]
Papa r12 industrial (A potato variety)	0,25 [0,84;-520,21]
Yuca llanera (A yucca variety)						1,26 [0,83;-466,09]
Coco (Coconut)		2,46 [0,77;-679,96]
Papa pastusa (A potato variety)	0,29 [0,76;-527,16]
Cebolla cabezona blanca (An onion variety)					0,94 [0,75;-530,23]	2,04 [0,69;-538,78]
Papa criolla lavada (A potato variety)				2,14 [0,71;-544,25]		2,21 [0,74;-539,7]
Papa criolla sucia (A potato variety)				1,84 [0,69;-543,3]		1,86 [0,71;-540,95]
Auyama (A pumpkin variety)					1,57 [0,69;-463,64]	1,78 [0,69;-464,09]
Limon tahiti (A variety of lemmon)		2,34 [0,61;-600,09]	2,71 [0,6;-600,96]	3,22 [0,59;-556,97]
Garlic (Garlic)			6,51 [0,59;-682,73]
Curuba boyacence (A variety of passiflora tarminiana)					1,36 [0,56;-506,34]	1,89 [0,58;-504,59]
Maracuya (Passiflora edulis)					2,12 [0,51;-563,6]

¹Hedge ratio, in brackets first R2 and then Log-likelihood. Only models with R2 ≥ 0,5 are reported.

Appendix E.

Table A6.

Hedge ratio estimated with Eq. (1) and regressors lagged variables.

Agri-product/Contract	FE2	FE3	FE4	FE5	FE6
Cebolla cabezona blanca (An onion variety)					0,34 [0,76;-2,79]
Papa criolla lavada (A potato variety)					0,37 [0,63; 11,13]
Curuba boyacence (A variety of passiflora tarminiana)			0,25 [0,61; 31,92]	0,22 [0,6; 30,31]	0,32 [0,62; 32,01]
Curuba san bernardo (A variety of passiflora tarminiana)		0,24 [0,53; 20,44]	0,22 [0,54; 20,7]	0,27 [0,54; 20,63]	0,32 [0,56; 21,84]
Papa criolla sucia (A potato variety)					0,37 [0,54;-8,57]
Feijoa (Feijoa)	0,191 [0,52; 21,67]

¹Hedge ratio, in brackets first R2 and then Log-likelihood. Only models with R2 ≥ 0,5 are reported.