Chapter One Draft

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Price volatility and international trade: Some reflections for importantcommodity exporters

Introduction

Commodity prices tend to be subject to high volatility. This high volatility tends to be explainedmainly, but not only, by supply side effects such as climate in the case of agricultural products.However, this volatility can be also explained by Government measures or other internationalinstitutions (OPEP decisions in terms of supply of oil, for example). Moreover, demand side effectscan be also found such as changes in the income and production structure of the important buyers,such as China and India in the last years. On the other hand, Governments can reduce or amplify thisvolatility with different policy measures (import and export tariffs, subsidies, buffers, etc). Since thevolatility is transmitted between countries, international trade must be considered in the analysis.

The effects of high volatility are greater the larger the share of the agricultural and mining activities inthe economy or in exports but also the lower or weaker the market tools or institutional arrangementsavailable to reduce them, such as future, assets and insurance markets. Moreover, high volatility couldalso affect the Governments budget as well as the current account of the balance of payments.

It is well recognized in the literature and in the economic history the effects of phenomena such as theso-called Dutch Disease. However, continuously countries have been experiencing problems indealing with this phenomenon. Sudden increases in commodity prices tend to reduce the relativeprofitability of other economic sectors, reducing its participation in the total product andconsequently, making the economy even more vulnerable to the following reduction in the price. Thisphenomenon reinforces the observed volatility, increasing prices when they are already high andreducing them further when they are already low. On the other hand, Governments have been several

times incapable of dealing with these problems.

It is convenient to clarify what is the problem. At the end, developing countries have been alwayslooking for higher prices for their exports and blaming developed countries about protectionistmeasures that reduce the international price, particularly in agricultural products. Since the 1950s and1960s several economist have been warned about the declining price in the agricultural and miningproducts. Prebisch and other economist from the Structuralism School have been warning about thisproblem. However, they do not foresee that also industrial products would also fall, making thedeterioration of the terms of trade not so important. Nevertheless, the bias against the agriculturalproduction and pro industrialisation has been and it is present in the development literature. However,it seems that the problem is not the constant deterioration of the terms of trade or reduction for theprices of exports. The main problem is seems to be that commodities in general, even though could befacing a downward or upward trend; they are subject to sudden increases and decreases. In a nutshell,more than the trend, the problem is the variance.

From 2003 until nowadays, prices for commodities have increased again. Whatever the causes behindthese increases, the problem seems to appear again. Commodities producers are facing againextraordinary higher prices for their products and the possibility that problems could appear if pricesfall is latent. Moreover, it seems that institutional capability to deal with these problems has notimproved and the danger is still present. In some cases, countries are applying old recipes to deal withthe problem and some questions raises about the efficiency and effectiveness of that measures.

This is a problem particularly of economies in which the agricultural, mining and oil activities play animportant part in the total economic activity or in countries in which their exports rely heavily on thiskind of problems. If we accept that agents try to smooth their income and, specially, theirconsumption, price volatility constitutes an impediment to achieve that goal. This appears particularly


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when agents do not count with appropriate market tools to hedge against this movements and transferwealth and income from states of nature and across time, they are unable to smooth their consumptionand are subject to the consequences of the price volatility.

If the market tools are available, producers could reduce, in principle, their exposure to the highvolatility prices, but also, they could reduce the volatility in itself. If insurance, futures and assetsmarkets are available and their work efficiently, producers could transfer wealth between time andstates of nature. This would contribute to reduce the price volatility and consequently, the economiccycle volatility and reduce the whole economy risk exposure.

On the other hand, there is a policy dimension. Governments could reduce price volatility and smooththe economic cycle by using appropriately different policy instruments. However, the experiencereveals that they could not achieve the stabilisation of price and sometimes, they have also worse theproblem. One question to answer is that if their failure has been due to the tool chosen in it or due toan inappropriate use of it.

Related to the previous point is the use of trade policy to deal with this phenomenon. In the case of

Argentina, for example, being an important exporter of food products, the increase in the commoditiesprices adds another problem to the phenomenon, since it tends to increase prices for food in thedomestic market. That means that since agricultural exports explain nearly 50% of total exports,increases in international prices tend to increase also the domestic price in sensitive products. TheGovernment solution has passed to isolate the export market and the domestic market by theintroduction of export taxes and export restrictions. On the other hand, countries facing lowinternational prices tend to increase tariffs to protect local producers and increase their profitability1.

This adds the main contribution of this paper: the international trade dimension. During the 1970s theAcademia showed a renewed interest in the study of the price fluctuations determinants and the toolsthat agents can use to reduce or hedge from that volatility. Particularly, authors such as (QUOTE)developed different analysis tools However their analysis have focused on the analysis in a single

market framework. In their analysis, there is only one good, homogenous suppliers and consumers.However, we see in the real world that more frictions are present. Tariffs, distances, transportationcosts and tastes add different implications to the problem. This generates also the possibility of exchanging risk across suppliers and consumers in the form of the international trade. Producersfacing low prices in their own market can increase the exports in order to smooth their incomes. Thisdimension must be considered in the analysis.

The goal of this paper is to analyse how the international and the domestic prices behave whenmarkets are subject to output shocks and when the economy is integrated in the world. This impliesthat rather one market for each good, we have national markets that are related each other in aninternational market. As consequence, the international trade constitutes another dimension thataffects the international and domestic volatility. In order to achieve that goal, a dynamic model ispresented in which we have two countries that are subject to different type of output shocks. Themodel relies on (Turnovsky S. J., 1983)s work in terms on how the production decisions are madeunder shocks. However, several authors before and later had been working in similar frameworks.Nevertheless, they did not consider, at least to some extension and to our knowledge, the internationaltrade dimension that this paper includes.

However, the research agenda for this topic is complicated. The introduction of international trade inthis kind of model and the introduction of imperfect substitutability between origins of products(imported and domestically produced) complicates the mathematical solution since we are departingfrom the linear models utilised before. As a consequence, this paper more that clarifying the questionseems to complicate more the analysis. The reader of this paper will have a bitter taste since a several

1 In fact, under the WTO agreements, countries can applied safeguard measures if import prices fall below a pre-established threshold or if there is an important import surge.


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questions will be presented without almost any answer. The answers are expected to be present infurther stages of this research. However, this paper highlights that the problem in question is morecomplicated and depends on several factors omitted before. However, the idea of this paper is not toanalyse how volatility behaves in the presence of trade but given that trade exists, how the volatilitychanges when some elements that affect trade vary.

It is also convenient to clarify that this paper is the first part of a long research agenda. Particularly,this paper does not include other important determinants of the volatility of prices that have beenincluded before in this literature. They are expected to be part in further research stages that willintegrate the international trade dimension with other features in the analysis of price volatility.Moreover, the model developed here has the flexibility to include additional considerations. These areexpected to be present in later stages of this research.

The first part of this paper will present the model that will be used to analyse the market behavior.From very simple assumptions, a very simple and clear model was developed that can be used toanalyse any commodity market. However, due to incorporation of some non-linear functionsnecessary for the trade dimension, the mathematical solution is hard to achieve. As a consequence, we

have decided to implement this model in standard mathematical software and allow it to speak. Thesecond part of this paper presents the data and the calibration techniques used in the simulations. Withvery little quantity of data that reflects the international supply and demand conditions for threegoods, we were able to implement this model and obtain interesting results. The third part of thispaper presents some simulations and sensitivity analysis on three key parameters: the elasticity of demand, the coefficient of risk aversion and the elasticity of substitution between imports anddomestic good. This exercise allows us to analyse how the model behaves under different structuralparameters that will shed some light on how the price volatility is transmitted between countries. Thefinal part will draw some conclusions and set the starting point for further research.

An export country dynamic model

During the 1970s and 1980s there was a bloom in the interest on the analysis of how markets behaveunder uncertainty. This literature, besides stochastic analysis elements, introduced definitely thedynamic analysis in economics. However, this literature basically continued a research avenue thathad started several years before, particularly, in the discussion of expectations in economics.(Nerlove, 1958) and (Muth, 1961) constitutes two seminal works in the development of expectationsand dynamics in economics.

The dynamics and the expectations are clearly related concepts. Necessarily, expectations will affectthe dynamic conditions. As (Muth, 1961) states: ...the character of dynamic processes is typicallyvery sensitive to the way expectations are influenced by the actual course of events. As aconsequence, different expectations will generate different type of dynamic phenomena.

The literature that surged in the 1970s and 1980s was definitely based on the (Muth, 1961)sapproach or rational expectations approach. The idea of that the expected price is an unbiasedestimator of the price 2 resulted extremely appealing and theoretically well founded. As a contrary, theadaptative expectations approach, typical of cob-web phenomena, was deemed as naive and it wasconsidered that agents should make the most efficient use of the information and, in the case of adaptative expectations, of the previous prediction errors. (Muth, 1961) puts it very clearly...dynamic economic models do not assume enough rationality

From the rational expectations approach, a very rich literature appeared that try to analyse howmarkets behave under uncertainty and given the expectations what are the price and quantity

dynamics. Given the high volatility in commodity prices during the 1970s, it was recognised the2 If disturbances are normally distributed.


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importance of designing tools to help to stabilise those prices. As a consequence, part of the academiafocus on the analysis the implications of storage in rational expectations models (Wright & Williams,1982) , (Wright & Williams, 1984) and (Scheinkman & Schechtman, 1983) , buffer mechanisms(Newbery & Stiglitz, 1979) and (Newbery & Stiglitz, 1981) and futures markets (Turnovsky S. J.,1979) and (Turnovsky S. J., 1983). However, despite the reduction on the interest in the research of this topic, several authors have been continuing this research avenue in the following years. (Deaton& Laroque, On the Behaviour of Commodity Prices, 1992) and (Deaton & Laroque, 1996) in partialequilibrium and (Hirshleifer, 1988) and (Hirshleifer, 1990) under a general equilibrium approach.Also, some developments departing from the rational expectation approach (Westerhoff & Wieland,2004) and more applied to agricultural products and in general equilibrium framework, (Bourguignon& Sylvie Lambert, 2004)

This literature shared several common features. As was mentioned, they made an extensive use of rational expectations. As a consequence, the profit maximising behaviour of producers was alwayspresent. 3 They tend also to be based in partial equilibrium frameworks and, as a consequence, theydid not consider the effects that substitution across commodities in the production decision couldhave, particularly in the agricultural sector.

The most relevant, in terms of this paper, was the omission of the effects that trade could have in thevolatility of prices. This literature analysed the behaviour of markets without considering anyinteraction between similar markets in other countries and the effect on the international price. Sincethe trade dimension was not considered and only one market was considered, the interaction betweendomestic and international prices was omitted. As a consequence, there was not any distinctionbetween foreign and domestic instabilities.

It is interesting to see that the possibility of different paths and variation for domestic andinternational price was not considered in this literature, given the theory and evidence provided in thetrade literature of a disconnection between both prices. Despite several seminal trade theoriesconsidered that domestic and foreign prices should converge, latter theory developments as well as the

evidence suggest several departures from this idea, even for tradable goods. The most importantconsideration and relevance for this paper is the idea of imperfect substitution between domestic andimported goods (Armington, 1969) However, the possibility of imperfect substitution betweendomestic and imported good has been considered and analysed in more static type of analysis and,generally, in general equilibrium frameworks (Dervis, de Melo, & Robinson, 1982) and (Devarajan,Lewis, & Robinson, 1993).

Furthermore, it is the objective of this paper to develop a model that tries to include trade and theimperfect substitution between domestic and imported goods as another dimension in the pricevolatility. Moreover, it will try to analyse how the markets behave when consumers or importers aremore or less prone to substitute domestic goods and imports.

We will use (Turnovsky S. J., 1983) framework and we will add the trade dimension to thatdevelopment. The reason lays, basically, on the clarity of exposition and development of that work.Moreover, despite the analysis we are presenting here does not consider the existence of storage andfutures markets 4, (Turnovsky S. J., 1983) is originally intended to analyse, particularly, those features.As a consequence, it will be later easier to add them to this model.

3 However, some have claimed that farmers, instead of maximising profits, they could try to minimise risk

(Newbery & Stiglitz, 1981). 4 Storage and future markets will be considered in a later stage of this research.


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Let us assume a producer that sells to the international and the domestic market. We assume that theproducer operates under a quadratic cost function 5. Its profit function in t can be represented by

1) = Where q is the planned output chosen by the firm or producer, t q is the actual output of the firm and is the spot composite price for its output at time t . Note that the cost does not depend on the actualoutput but on the planned output. The idea is that this producer will decide how much he will produce;face the cost of producing that planned output but, the actual output is stochastic. We will assume thatoutput is subject to an additive technological risk, where t is a stochastic disturbance with zero meanand known variance:

2) = + The model could handle a multiplicative type of technological risk (with mean equal 1 and knowvariance). However, the introduction of multiplicative risk will complicate the analysis in later stages

of this research. Particularly, when multiplicative risk is present, the hedging and output decisionscannot be separated or the Separation Theorem does it hold (Danthine, 1978). As a consequence, wedecided to keep the additive risk specification despite it can be considered not the best option foragricultural goods (Newbery & Stiglitz, 1981).

The main contribution in this model, as it was mentioned, is that now the producer can supply eitherthe international or the domestic market. As a consequence, its planned output can be divided intoplanned exports and planned domestic supply.

3) = + Where and are the planned exports and planned domestic supply. As a consequence, the exportand domestic supply decisions are determined when the output decisions are taken. This can beexplained for example by the existence of contracts for exports and domestic supply. Rather thandecide how much to export and how much to sell domestically after they have decided how much toproduce; the operation tend to be the opposite. The total output is defined by the commitments onexports and domestic supply. Of course, after the shock is revealed, the exports and the domesticsupply could vary from his planned levels.

We can define the average composite price as the weighted (by the planned supply levels) average of the international and the domestic prices.

4)

=

Where et P is the international or World price andd

t P is the price in the domestic market. Both priceswill be determined by the interaction of the domestic and the international demand. The firm makesits production decision at time t-1 , before the prices are revealed. Furthermore, the profit function canbe expressed as

5) = + 5 The possibility of more elaborated cost functions were not considered, however, a linear cost function willeventually generate an indetermination in the model.


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The firm maximises the following one-period function of the expected profit and variance. This utilityfunction depends positively on the expected profit and negatively on the variance of the profit. In thissetting, the utility of the producer is reduced by the volatility of the profits.

6) )1,(21)1,(* 2 = t t at t t

Where, )1,(* t t = )(1 t t E is the conditional expectation of profit at time t formed at the previous

period; ( )( )2112 )1,( t t t t E E t t = is the conditional variance of profit at time t formed at t-1 .In this special form, a represents the producer risk aversion. When it equals zero, the producer is risk neutral and the variance term disappears from its expected profit function. If a is greater than zero,the producer is risk averse. The bigger is the coefficient of risk aversion, the more importance will bethe variance of the profits in the producers utility function. The expected value of the profit and theexpected variance 6 can be expressed as

7)= = , +

8) = , 1+2 , + Finally, replacing the expected profit and the expected variance in equation 6, we will get theproducers utility function expressed in terms of the mean and the variance of the profits.

9) = , + , 1+2 , +

Again, if the producer is risk neutral, the variance term vanishes and only the expected value of theprofits can alter the level of utility achieved. Continuing with (Turnovsky S. J., 1983) development,we will assume n identical firms or producers and each of them contributes equally to the totaldisturbance 't , as a consequence, for the representative firm nt t ' = . Additionally, if we assumethat the price responds proportionally to the total supply stochastic disturbance 't , then crossmoments formed at t-1 between and 't are finite and of order 1. Furthermore, we will have that

, 1= 1

=1

= 1

, =1 , = 1 , 1=1 = 1 Where, ( )*O denotes order. Assuming that the number of producers is large, the terms with order lessthan one will tend to vanish and a consequence and to the first order, we can express the one periodmean and variance of profit by

10 = , 6 See Annex I


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11) = , 1 Replacing these two expressions in expression 6 we will get, for the representative producer that,

12)

= , , 1

Now, we are in position of finding the export and the domestic product supply function. The plannedexports can be found by differentiating equation 12 respects to , the planned exports.

13 = ,+ , 2 , 1+ , From equation 4 we can clearly seen that

,= , + ,+ Where ,and ,are the conditional expectations for the international and the domestic pricesformed at t-1 , respectively. Taking its derivative respect to qis

,= , + ,+ + ,+ Or14 + ,= ,= , , + ,= ,+ , Now, the variance of the composite price, expressed in terms of exported and domestic suppliedquantities can be defined

, 1= + , 1+ + , 1+2+ , Where, , 1and , 1 are the conditional expected variances for the internationaland the domestic price formed at t-1. Its derivative respect to

is

, 1= 2 , 1+ , 1+2 ,++2 , 1+2 ,+ 15) + 22 , 1= 22 , 1= 222+ 22+2 ,+ +22+2 ,

Now, replacing equations 15 and 14into equation 13 we get


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16) = , + , Where we have replaced , 1by to save notation. Working in the same way we can getthe derivative respect to 17) = , + , As a consequence, the planned exports and domestic supply can be written as

18) = , , 19)

=, ,

The planned supply of exports and domestic product depend on the respective expected prices as it isexpected. As it is also seen in similar developments, it also depends negatively on the variance of theprice. i.e. a higher variance will reduce the supply of the product. The new element in this expressionis the expected covariance between the two prices. In fact, the role of the covariance in thisspecification is extremely relevant. If the expected covariance is positive and the producer is risk averse ( a is greater than zero), the producer will find profit maximising to increase its supply of theproduct in question since it cannot reduce their risk exposition by supplying the other product. On theother hand, if the expected covariance is negative, the producer will reduce its supply in the product inquestion since it will prefer to take a more diversified position. That implies that any increase in theexpected price will not be translated into an increase in the supply of that product and would generatean increase in the supply in the other product by the action of the covariance.

We need now to add over the total number of producers. Since we are assuming homogenousproducers, we can multiply each supply function (equations 18 and 19) by the total number of firms orproducers. We must consider that now, the supply of both exports and domestic supply will beaffected by the total output disturbance, 't . However, the total output disturbance affects the totaloutput and we have divided the problem into two supply decisions. As a consequence, we need toassign how the total output disturbance will affect each supply decision. We will assume that the totaloutput disturbance is split between both products (exports and domestic supply) by the share of theplanned exports/domestic supply in the total planned output.

20) = , , +'t

21 = , , + Where is the total supply of exports, is the total supply of domestic product, = and

=.


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We will not turn to the demand side. We will assume that the demand is supplied with domesticsupply and imports. Moreover, we will further assume that the demand is completely deterministicand does not depend on any type of shock. This is also a common feature in this type of literature anddespite some analysis on the effects of volatility in the demand (Newbery & Stiglitz, 1979), ingeneral, the greatest sources of volatility tend to come from the supply side. We will use a nestedstructure to model the demand system. On the top of the nest, the total demand is determined by thecomposite price between the price of the domestic supply and the international price.

22) = 0, > t C Where is the total demand for the product and is the composite demand price. As wementioned, the total demand is composed of domestic supply and imports; as a consequence, we needa proper definition on how the consumer will allocate its demand of domestic supply and imports. Wewill use make use of the well known Armington assumption (Armington, 1969). The assumptionbasically establishes that consumers perceive imports and domestic supply as two goods with alimited degree of substitutability. This is specified through a Constant Elasticity of Substitution (CES)

function. The composite price is defined as the weighted average of the domestic and the internationalprice.

23) = The Armington aggregator is defined as

24 = +1 =1Where G is the shift parameter, is the share parameter and is the elasticity of substitutionbetween domestic produced demanded and imported products. The minimisation of the expendituregives the following first order condition

25= We have almost all the equations necessary for our model. We need now to establish our equilibriumcondition. Up to this point, we have developed our model without making any assumption about howmany countries are in our world. We will assume that there are two countries: Home and the Rest of the World (ROW). The technology of production and the demand structure is similar across the twocountries. However, we will assume that the two countries are subject to different shocks. In essence,the same type of additive shock will be applied; however, we assume that the standard deviation of

the shock is different. This could be seen as, for example, both countries being subject to differentweather shocks. We will assume also that the two shocks are not correlated.

On the other hand, we will assume that the Home country is a pure exporter and it will not importfrom the ROW. As a consequence, the ROW imports all its exports plus the exports from HOME.This implies that we need two equilibrium conditions. On one side, the domestic demand and thedomestic supply at Home must equal; and, on the other hand, the exports and imports must be cleared.These conditions are expressed as follows, where we have used the double superscript to distinguishHOME and ROW magnitudes.

26 , = , 27 , + ,= ,


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In order to have a clear idea of how this model behaves, we have implemented it in GAMS.Furthermore, we present the Table 1 all the equations in the model as it was implemented in GAMS.We have also included as separate equations the expressions for the different expected values forprices, variances and covariance since they will be updated each period in the model solution.

Table 1. Model equations

Q= nP,qcaCOVP,Pc+a +'t = +1 Q= nP,qcaCOVP,Pc+a + = 1 = = = 1 = = 1 = = 1 = = 1

,=

, , 1= 1 , + ,= ,

, 1= 1 , = t1 The behaviour

In this section, we will explain what would be the sequence of effects after a once increase in thesupply of the commodity in both HOME and ROW. The idea of this exercise is try to capture the

intuition behind the model and later, we will present the results of the simulations performed. We willassume that there is a single shock in a given period and we will explain how the model behaves afterthat shock.

Suppose that in a given period, due to an extraordinary benign weather conditions, there is an increasein the supply of any of the commodities at ROW. As a consequence of the shock the supply of exportsand domestic product at ROW increase by equations 20 and 21. The distribution of the effects in bothsupplies is determined by the variable that captures the share of exports or domestic supply in totaloutput. The increase in the supply generates an immediate reduction in the domestic price at ROWand in the world price for this product. What is the effect at HOME? When HOME producers decidedtheir output and supply, they did not foresee the shock. Furthermore, their level of output in the periodof the shock is equal to the equilibrium or previous level. Moreover, the domestic and export supplydecisions were made without the shock. As a consequence, they do not change in this period. HOMEproducers behave as the shock would not have existed. One can think that there were supply contractsin place at the time of make their decisions that cannot be broken when the international price falls.Furthermore, there is no effect in the period of the shock at ROW for HOME. However, theinternational price has fallen revealing the increase in the availability of product. The increased supplyof exports made by ROW is entirely absorbed by ROW as imports. As a consequence, the totaldemand at ROW increase strongly (by the increase in the domestic supply and the increase in imports)

In the following period, both HOME and ROW producers include the previous period information intheir price expectations (and expected variance) formation in order to make their output decisions forthe current period. Since the previous international and ROW domestic price have fallen, the expected

prices have also fallen. Moreover, the expected variances of both prices are positive now at ROW.The expected covariance between the domestic price and the world price at ROW is now positive butremains zero for HOME (this is because, the domestic price at HOME did not change) Furthermore,


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ROW producers reduce their supply of both, exports and domestic products. This holds except forHOME. The HOME producer includes the new international price information in its price formationwhich makes the expected price to fall and their expected variance to rise. However, the domesticprice at HOME did change in the previous period and, consequently, neither the variance nor theexpected domestic price change. Furthermore, at HOME all the adjustment is made by reducing thesupply of exports rather than reducing the supply of the domestic product. As a consequence, theROW producers adjust down the supply for exports and domestic product while HOME producersonly adjust the supply for exports. Furthermore, the international and the ROW domestic spot pricerise.

In the third period (counting from the shock), the new price information of the second period isincluded in the price and the variance expectation of the producers. At ROW, the supply is increasedbecause the expected price of both, exports and domestic product has risen. At HOME the exportssupply is increased but also the domestic supply is increased. This occurs basically because thesubstitution between domestic and export market is not perfect and part of the extra output is allocatedalso in HOME market. Moreover, the covariance between both prices has also changed and also theexpected output of the exported product has also changed and this affects also the supply of the

domestic product. Furthermore, the producer decides to hedge against the fluctuations in theinternational market by increasing it supply in the domestic market. As a consequence, the spot pricein the third period in the domestic market at HOME is reduced. Furthermore, the adjustment in thedomestic market at home begins three periods after the shock.

In the fourth period after the shock, again the previous prices are included in the price expectationformation. Now, the expected domestic prices and the international price have fallen , as aconsequence, the supply of exports and domestic product in both, HOME and ROW is reduced,bringing the spots domestic and international prices up. Since the domestic price at HOME has fallenin the domestic market in the previous period, it will affect the price expectation for the domesticprice for this period and the expected variance.

This sequence of adjustment continues in further periods. However, every period the adjustment issmaller until the variables will converge eventually to the new equilibrium values when the initialshock is washed in the history. A similar process occurs when the shock is originated at HOME,however, in the ROW both exports and the domestic supply response are lagged one period. However,the domestic price at ROW will be affected in the first period. Since ROW is the only importer in thismodel, the extra export supply of HOME is absorbed by ROW and as a consequence, the supply isincreased at ROW generating a decrease in the domestic price.

The size, speed and type of adjustment depend on several factors. First, it is important the relative sizeof each country in the commodity market analysed. If the shocked country is a small supplier, theshock will have little incidence in the world market and will not affect substantially the other countrydomestic market. Moreover, it will also affect the importance of the exports in the countrys supplyscheme. Products that are heavily exported will have a different effect if they are mostly consumeddomestically. On the other hand, the effect could be different if the country is an important producerbut also an important consumer, since any decrease in the domestic demand could have importanteffects in the international market.

Second, the demand will also play an important role. In the case of very inelastic demand functionsthe price in the domestic market, the quantity demanded will change very little. In that case, weshould expect, a priori, that the volatility of the international price must be increased because thedomestic market is not adjusting enough and any excess of supply will be transferred to the internalmarket.

Third, the risk aversion of producers will also affect the supply response. When the producer isextremely risk averse, he will make a lower adjustment of the supply since the supply depends


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negatively on the variance of the price. If this is increasing, a risk averse producer will react stronglycompared to a risk lover.

Finally, the adjustment will also depend on the flexibility by which the consumers in ROW cansubstitute the domestic and imported product. If the consumers consider both products (the domesticand the imported) as not substitutable, it will not be possible to switch output from one market to theother in order to reduce the volatility of the producers income. On the other hand, if the importersconsider both products as perfect substitutes, the volatility of the domestic and the international pricewill be similar.

Given the non-linearity of some functions, it is hard to find an analytical solution to the model thatcould shed some light on the behaviour of the model. As a consequence, we have decided to let themodel speak by making simulations of it using GAMS. We will simulate later how this modelbehaves under different values for the elasticity of demand, the coefficient of risk aversion and theelasticity of substitution between domestic product and imports when there are shocks coming fromHOME and the ROW. Before, we will present the main data values used in the simulations.

Data and calibration

In order to simulate this model we have used real data on output to calibrate the parameters for thedistribution of the shocks. We have simulated this model using data for soybeans, maize and wheat. Inthis model, Argentina is represented by HOME. We have used Argentina as a case since it is animportant producer and exporter in some commodities. However, the model could replicate thesituation of other country.

The model implementation requires data to serve as a solution baseline. As a consequence, data onoutput, exports, imports and domestic consumption as well as the number of producers were obtainedto form a solution baseline. In the case of HOME, we have collected data on the commodity balancesfor the 2006/2007 Argentine campaign. The ROW data was taken from FAO FAOSTAT. In the caseof the number of producers, we have assumed homogenous producers. Furthermore, we proxy thenumber of producers by the number of hectares harvested. This implies that in this framework, thequantity of producers is represented by the number of hectares.

We have calculated all the data for the individual producer. Since producers are homogenous, weassume that each of them exports the same average quantity. As a consequence, we have calculatedthe export and domestic supply yield by the total yield multiplied by the share of exports and domesticsupply in total output. The total HOME exports, for example, can be calculated by multiplying theexport yield by the number of producers. Since we are assuming that the Home country does notexport, the sum of total exports of both countries, HOME and ROW, must be equal to the ROWstotal imports. The domestic demand must be equal to the domestic supply at HOME; and in the ROWthe domestic demand is equal to the sum of the imports and the domestic supply. We are notconsidering any other use (stocks, seeds, feeding, etc.). In Table 2 we present the quantities data used.From this very basic data, we construct all the quantities variables in the model.

Table 2 also have relevant information that can help to interpret the results. It can be seen that atHOME, Maize is the most exported product with nearly 63% of the output exported. On the otherextreme, Soybeans is a product that is the less exported (21%). In fact, in Argentina, the soybeansoutput is mostly used to produce oils and meals that are latter exported. However, we are notconsidering other use than exports and domestic demand, that could be final consumption or industrialuse. On the other hand, we can see that the opposite occurs in ROW where the majority of the outputis domestically demanded. It can be seen, that HOME in maize supplies the 18% of the World

exports, 15% in soybeans and 6% in wheat. On the other hand, HOMEs production on maize


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represents 3% of the World production, 22% of the total production of soybeans and 2% of the totalproduction of wheat.

Table 2. Quantity data used in baselineVariable Unit Home ROW

MaizeTotal Yield Metric tonnes/hectare 7.665 4.844Export yield Metric tonnes/hectare 4.880 0.4347Domestic supply yield Metric tonnes/hectare 2.785 4.4093Number of producers thousands 2,838.072 142,660.835

SoybeansTotal Yield Metric tonnes/hectare 2.971 2.163Export yield Metric tonnes/hectare 0.640 0.7061Domestic supply yield Metric tonnes/hectare 2.331 1.4569Number of producers thousands 15,981.264 77,412.175

WheatTotal Yield Metric tonnes/hectare 2.625 2.845Export yield Metric tonnes/hectare 1.300 0.5087Domestic supply yield Metric tonnes/hectare 1.325 2.3363

Number of producers thousands 5,540.405 215,897.814Source: Author calculations based on FAO FAOSTAT and Rodolfo Franks database and the Secretariat of Agriculture, Livestock, Fisheries and Food Industry.

As a consequence, the baseline value for the total expected supply of maize, for example, can becalculated as Export yield times the number of producers. In the baseline, the domestic prices and theinternational price are equal and set to unity. This is allows an easier interpretation of the results andfacilitates the calibration of the model.

The elasticities of demand, substitution between imports and domestic product at ROW and thecoefficient of risk aversion play an important role in this model. We do not have accurate estimationsfor them. However, we have decided to play with them in order to analyse the model properties under

different values of these. They will also play an important role in the calibration of the model. Forexample, the share parameter in the CES function is calibrated using a given value of the elasticity of substitution. As a consequence, each time one of this parameter is changed, there is a correspondentchange in another parameter.

Results

The simulations of the model were made using GAMS. We have simulated a 25% increase in theoutput for each product in both, HOME and ROW in the 5 th period. However, the shock applied toeach country is considered an independent exercise. The model can be solved for several periods,however, for the sake of the exposition we limited the time periods to 20. This is basically due to thefact that as more periods are included, it is hard to see the effects since the effects as washed away inso many periods and also, because the computing time increases. As a consequence, in this timeframe, variables will not reach completely their new equilibria. We will present the results underdifferent elasticities of demand, different coefficient of risk aversion and different elasticities of substitution between domestic products and imports. In the Annex II we present the description of theexercises performed.

Elasticity of demand

In this exercise we have simulated the model using different elasticities of demand at HOME but

keeping fixed the ROWs elasticity of demand across simulations. Moreover, we have performed toseparate sets of simulations: one for shocks that are originated at ROW and one for shocks that are


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originated at HOME. The solution found by (Turnovsky S. J., 1983), which is analogous to thesolution found by (Turnovsky S. J., 1979), (Kawai, 1983) and (Muth, 1961) is that we should expectthat a high demand elasticity reduces the price volatility (expressed as the variance of the spot price).Table 3 presents the coefficient of variation of the domestic price in both countries for every scenarioconsidered when the shock is generated in ROW. As it is expected, different elasticities of demand atHOME has very little effect in the volatility of the domestic price in ROW. However in HOME thepicture changes dramatically. As we increase the value of the elasticity of demand (from inelastic toelastic values) the volatility of the domestic price is substantially reduced. For example, doubling theelasticity of demand from 0.6 to 1.2 will reduce the coefficient of variation of the domestic price by a25% in the case of wheat (compare 0.466 and 0.354), by 48% in the case of soybeans and by 40% inthe case of maize.

We have also made a similar exercise but simulating an increase of the 25% in the output at HOME. Itis expected that the effects will be bigger at HOME than in the ROWs domestic market. Table 4presents the results. As we increase the elasticity of demand, the coefficient of variation of thedomestic price at HOME is reduced in all cases. If we double the elasticity of demand from 0.6 to 1.2,for example, the volatility of the domestic price is reduced by 60% in the case of wheat. These results,

furthermore, do not differ from the ones we obtained when we simulated a shock coming from ROW.There are not important changes in the coefficient of variation of the domestic price in ROW forwheat and maize, but the coefficient of variation for the domestic price of soybeans change as wechange the elasticity of demand at HOME. Moreover, from Table 5, we see that the World price isaffected differently according to the elasticity of demand at HOME. This is a very interesting result.By looking in the data values we have used, we can realise that soybeans is a product that is largelyconsumed domestically 7 and given that HOME is an important producer, any change in the domesticmarket will have important effects in the international market and, consequently, in the domestic priceat ROW. What is also very interesting is the U-shape behaviour. Initially, when the elasticity of demand at HOME is increased, the domestic demand at home adjusts faster to the price. This helps tostabilise the domestic price at ROW since HOME can easily reallocate any surplus into their domesticmarket. However, when the elasticity of demand is big enough (particularly when is bigger than one),

the higher elasticity in the demand at HOME generates substantial swings of supply from the exportmarket to the domestic market, generating an increase in the volatility of the international price andthe volatility of the domestic price at ROW. This contradicts the results found by (Turnovsky S. J.,1983) since now; there are other factors that could be affecting the volatility in the price. In this case,the volatility of the domestic price at ROW is being affected by the elasticity of demand at HOME.

Finally, in Table 5 we present the volatility of the international price for each scenario. When theshock is generated in the ROW, it does not have substantial influence the size of the elasticity of demand at HOME, even if HOME is an important player in the market. This is also explained by thefact that ROW can absorb any increase in the supply in their market. We must remember in this case,that ROW is the only importer in this model and is the only one that imports their exports. As aconsequence, any sudden increase in the supply is almost completely absorbed in ROW. If the shock is generated at HOME, we see that there are not important changes in the coefficient of variation of the International price in both, wheat and maize. However, as the elasticity of demand at HOME isincreased, the volatility of the international price of soybeans also increases. This behaviour is similarto the domestic price at ROW that exhibits a similar pattern.

As a consequence, the unambiguous reduction in the volatility when the elasticity of demand isincreased seems to be challenged when countries are allowed to trade. It seems that in goods whereone of the countries is an important producer but it consumes largely their production, very high aswell as very low elasticities of demand, could generate important volatility in the World price. Thiscould be explained by the fact that when the elasticity of demand is very low at HOME and there is ashock in that country; the international market suffers since HOME producers reduce their export

7 In the case of Argentina, soybeans are used in the production of oils and meals that are later exported, but inthe case of unprocessed soybeans, the share of exports is smaller.


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supply in order to satisfy the inelastic and important HOME demand. However, when the elasticity of demand is very high at HOME, the high volatility in the domestic demand is transferred to the Worldmarket and since HOME is an important producer and consumer, a reduction in the domestic demandwill generate an important export surplus that will eventually increase the volatility in the Worldmarket. The relationship between the supply and demand composition and the volatility is expected tobe analysed analytically in a later stage of this research.

Table 3. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of elasticity of demand at HOME when shocks are generated in ROW

Wheat Soybeans Maize

Simulation HOME ROW HOME ROW HOME ROW

beta06row 0.466 1.924 0.107 1.698 2.103 2.207

beta07row 0.444 1.924 0.094 1.698 1.919 2.207

beta08row 0.423 1.924 0.084 1.698 1.762 2.207

beta09row 0.404 1.924 0.076 1.698 1.627 2.207

beta10row 0.386 1.924 0.070 1.698 1.510 2.207

beta11row 0.370 1.924 0.064 1.698 1.410 2.207

beta12row 0.354 1.924 0.059 1.698 1.321 2.207

beta13row 0.340 1.924 0.055 1.698 1.244 2.207

beta14row 0.327 1.924 0.052 1.698 1.176 2.207

beta15row 0.314 1.924 0.049 1.698 1.115 2.207

beta20row 0.263 1.924 0.038 1.698 0.888 2.207

beta30row 0.198 1.924 0.026 1.698 0.637 2.207

beta40row 0.158 1.924 0.019 1.698 0.499 2.207

beta50row 0.131 1.924 0.016 1.698 0.411 2.207

beta60row 0.112 1.924 0.013 1.698 0.350 2.207

beta120row 0.060 1.924 0.007 1.698 0.185 2.207

beta240row 0.031 1.924 0.003 1.698 0.095 2.207


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Table 4. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of elasticity of demand at HOME when shocks are generated in HOME



beta06home 12.055 0.039 13.522 0.215 17.117 0.095

beta07home 9.561 0.039 9.515 0.204 12.924 0.095

beta08home 7.956 0.039 7.575 0.200 10.344 0.095

beta09home 6.836 0.039 6.374 0.199 8.626 0.094

beta10home 6.006 0.039 5.539 0.198 7.410 0.094

beta11home 5.364 0.039 4.916 0.198 6.506 0.094

beta12home 4.852 0.039 4.429 0.198 5.809 0.094

beta13home 4.432 0.039 4.036 0.198 5.253 0.094

beta14home 4.082 0.039 3.711 0.199 4.800 0.094

beta15home 3.784 0.039 3.437 0.199 4.422 0.094

beta20home 2.781 0.039 2.522 0.200 3.193 0.094

beta30home 1.824 0.039 1.655 0.201 2.072 0.094

beta40home 1.358 0.039 1.234 0.202 1.540 0.094

beta50home 1.082 0.039 0.984 0.202 1.226 0.094

beta60home 0.899 0.039 0.818 0.203 1.020 0.094

beta120home 0.446 0.039 0.408 0.204 0.508 0.094

beta240home 0.222 0.039 0.203 0.204 0.253 0.094

Table 5. Coefficient of variation of the international price under shocks at ROW and at HOMEROW SHOCK HOME SHOCK

SIMULATION WHEAT SOYBEANS MAIZE SIMULATION WHEAT SOYBEANS MAIZE

beta06row 3.58 1.95 22.24 beta06home 0.57 1.65 2.36

















Coefficient of risk aversion


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The coefficient of risk aversion plays an important role in the supply decisions in this framework. Bylooking into equations 20 or 21 it can be seen that the higher is the coefficient of risk aversion, thehigher will be the weight the producer will give to the variation and the co-variation of the prices intheir supply decisions. In order to see if effectively in our model the volatility of the price depends onthe coefficient of risk aversion, we have performed a similar exercise as in the previous section. Wehave performed two sets of simulations altering the value of the coefficient of risk aversion at HOME.One for shocks generated in the ROW and one for shocks generated at HOME.

Table 6 presents the results for the coefficient of variation in the domestic price under different valuesof the coefficient of risk aversion when the shock is generated at ROW. The model behavesdifferently according to the product considered. In the case of wheat (first column of Table 6), risk lovers producers generate lower domestic price volatility at HOME. As the variance of the domesticprice changed, risk lover producers adjust more their supply than more risk averse producers,furthermore, the fluctuations in the domestic price tends to be reduced. In the case of Soybeans, whereHOME is an important producer but a comparatively modest exporter, the volatility tends to bedecreased as producers become more risk averse. However, at extremely high values of the coefficientof risk aversion, the coefficient of variation is increased. In the case of maize, where HOME is an

important supplier of the world market, we see that when producers are risk lovers the volatility ishigh in the domestic price but also this holds if producers are extremely risk averse. As aconsequence, the volatility seems to be minimised when the coefficient of risk aversion is around one.Moreover, in the case of maize, the different scenarios also generate changes in the volatility of thedomestic price at ROW since HOME is an important supplier of ROW (column 6 of Table 6).

When the shock comes from HOME, its producers are the first to receive the shock and observe theprice volatility. It can be seen in Table 7 that when the coefficient of risk aversion is increased, thevolatility of the domestic price at HOME is increased in the case of wheat and soybeans (columns 1and 3 of Table 7). However, it applies the opposite in the case of maize where HOME is an importantsupplier of the World demand. In the case of wheat and soybeans, the shock has small effects in theinternational market and, as a consequence, lower coefficient of risk aversion generates lower price

volatility as the shock is mainly absorbed in the domestic market. In the case of Maize, HOME is animportant producer and a more important exporter. A large share of the total production is exported.When the shock is received, it has immediate effects also in the international market. A risk loverproducer will react strongly in both markets but with their reaction will also affect the volatility inboth markets. This effect in the international market affects also the volatility at HOME. If theproducer is risk averse, the reaction will be small in both markets. The international price will changelittle and the domestic price volatility will be smaller than under higher coefficient of risk aversion.

An important result is that, with the exception of soybeans, the domestic price volatility in ROW doesnot change substantially with changes in the coefficient of risk aversion at HOME. In the case of soybeans, the lower is the coefficient of risk aversion at HOME; the lower is the volatility of thedomestic price at ROW. As the volatility of the domestic price increase, risk averse producerssubstitute domestic supply by exports generating a bigger supply at the World market that helps toreduce the volatility in the domestic market at ROW. In the case of Maize and Wheat, this cannot beseen because their exports are already high and the marginal contribution of more exports does notchange substantially the picture.

Table .8 sheds some light on the effects on the international price and helps to understand the effectson the domestic prices mentioned before when the coefficient of risk aversion is altered. Shocks in theROW generate, by the size of the markets, higher shocks than HOME shocks. However, when weconsider different type of attitudes to risk at HOME, we have different effects depending on where theshock comes from. When the shock comes from ROW, the volatility of the international price isincreased as we have more risk averse producers at HOME. The effect is very small in wheat andsoybeans, but it is relevant in the case of maize, the heavily exported product where HOME has animportant share of the World market. Risks averse producers return the volatility created in ROWwith a bigger volatility in the international price.


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When the shocks are generated at HOME, the domestic price volatility is not so easily transmitted tothe international price. As a consequence, the volatility of this does not change substantially.However, in the case of soybeans, a lower coefficient of risk aversion at HOME can reduce thevolatility of the international price. This is because being HOME and important producer but also animportant consumer, any substitution between domestic supply and exports made by the producerswill have substantial effects in the international markets. Facing high volatility in the domesticmarket, risk averse producers, increase the supply in the international market that is showing a lowervolatility. As a consequence, we have found that there are potential cross effects between the attitudeto risk of producers in HOME and the volatility in the World price that would eventually affect thevolatility of the domestic price at ROW.

Table 6. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of coefficient of risk aversion at HOME when shocks are generated in ROW



cra_04row 0.163 1.924 0.036 1.696 3.580 2.175

cra_03row 0.166 1.924 0.035 1.697 3.231 2.178

cra_02row 0.168 1.924 0.034 1.697 2.898 2.180

cra_01row 0.171 1.924 0.034 1.697 2.580 2.182

cra01row 0.176 1.924 0.032 1.697 1.989 2.187

cra02row 0.178 1.924 0.031 1.697 1.715 2.189

cra03row 0.181 1.924 0.031 1.697 1.458 2.192

cra04row 0.183 1.924 0.030 1.697 1.218 2.194

cra05row 0.186 1.924 0.029 1.697 0.999 2.196

cra06row 0.188 1.924 0.028 1.697 0.808 2.198

cra07row 0.190 1.924 0.028 1.697 0.659 2.201

cra08row 0.193 1.924 0.027 1.697 0.574 2.203

cra09row 0.195 1.924 0.026 1.698 0.569 2.205

cra10row 0.198 1.924 0.026 1.698 0.637 2.207

cra11row 0.200 1.924 0.025 1.698 0.753 2.209

cra12row 0.203 1.924 0.024 1.698 0.893 2.211

cra13row 0.205 1.924 0.024 1.698 1.044 2.213

cra14row 0.208 1.924 0.023 1.698 1.197 2.215

cra15row 0.210 1.924 0.022 1.698 1.350 2.217

cra20row 0.222 1.924 0.020 1.698 2.061 2.226

cra30row 0.247 1.924 0.017 1.699 3.144 2.242cra60row 0.320 1.925 0.030 1.702 4.572 2.277

cra120row 0.463 1.925 0.081 1.707 4.603 2.318


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Table 7. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of coefficient of risk aversion at HOME when shocks are generated in HOME



cra_04home 1.814 0.039 1.629 0.206 2.090 0.094

cra_03home 1.815 0.039 1.631 0.205 2.089 0.094

cra_02home 1.815 0.039 1.632 0.205 2.088 0.094

cra_01home 1.816 0.039 1.634 0.205 2.086 0.094

cra01home 1.817 0.039 1.638 0.204 2.084 0.094

cra02home 1.818 0.039 1.640 0.204 2.083 0.094

cra03home 1.819 0.039 1.642 0.203 2.081 0.094

cra04home 1.819 0.039 1.643 0.203 2.080 0.094

cra05home 1.820 0.039 1.645 0.203 2.079 0.094

cra06home 1.821 0.039 1.647 0.202 2.077 0.094

cra07home 1.821 0.039 1.649 0.202 2.076 0.094

cra08home 1.822 0.039 1.651 0.202 2.075 0.094

cra09home 1.823 0.039 1.653 0.201 2.073 0.094

cra10home 1.824 0.039 1.655 0.201 2.072 0.094

cra11home 1.824 0.039 1.657 0.201 2.071 0.094

cra12home 1.825 0.039 1.659 0.200 2.070 0.094

cra13home 1.826 0.039 1.661 0.200 2.068 0.094

cra14home 1.826 0.039 1.663 0.200 2.067 0.094

cra15home 1.827 0.039 1.665 0.199 2.066 0.094

cra20home 1.831 0.039 1.676 0.198 2.060 0.094

cra30home 1.838 0.039 1.698 0.195 2.047 0.094

cra60home 1.860 0.039 1.775 0.186 2.014 0.094

cra120home 1.907 0.038 1.995 0.174 1.961 0.093


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Table .8. Coefficient of variation of the international price under shocks at ROW and at HOMEand different values of the coefficient of risk aversion

ROW SHOCK HOME SHOCK


cra_04row 3.57 1.94 21.30 cra_04home 0.57 1.75 2.36

cra_03row 3.57 1.94 21.36 cra_03home 0.57 1.74 2.36

cra_02row 3.57 1.94 21.43 cra_02home 0.57 1.74 2.36

cra_01row 3.57 1.94 21.49 cra_01home 0.57 1.74 2.36

cra01row 3.57 1.95 21.62 cra01home 0.57 1.73 2.36

cra02row 3.57 1.95 21.69 cra02home 0.57 1.73 2.36

cra03row 3.57 1.95 21.76 cra03home 0.57 1.72 2.36

cra04row 3.57 1.95 21.83 cra04home 0.57 1.72 2.36

cra05row 3.57 1.95 21.90 cra05home 0.57 1.71 2.36

cra06row 3.57 1.95 21.96 cra06home 0.57 1.71 2.36

cra07row 3.57 1.95 22.03 cra07home 0.57 1.71 2.36

cra08row 3.58 1.95 22.10 cra08home 0.57 1.70 2.36

cra09row 3.58 1.95 22.17 cra09home 0.57 1.70 2.36

cra10row 3.58 1.95 22.24 cra10home 0.57 1.70 2.36

cra11row 3.58 1.95 22.31 cra11home 0.57 1.69 2.36

cra12row 3.58 1.95 22.37 cra12home 0.57 1.69 2.36

cra13row 3.58 1.95 22.44 cra13home 0.57 1.69 2.36

cra14row 3.58 1.95 22.51 cra14home 0.57 1.68 2.36

cra15row 3.58 1.96 22.58 cra15home 0.57 1.68 2.36

cra20row 3.58 1.96 22.91 cra20home 0.57 1.66 2.36

cra30row 3.58 1.97 23.56 cra30home 0.57 1.63 2.36

cra60row 3.59 1.99 25.35 cra60home 0.57 1.52 2.35

cra120row 3.61 2.04 28.45 cra120home 0.57 1.35 2.35

Elasticity of substitution between domestic product and imports

In (Turnovsky S. J., 1983) and other authors analysed, the international trade dimension is notincluded in their analytical frameworks. They considered in their analysis only individual marketswithout making any distinction between domestic and export markets. As a consequence, they did notconsider the effects that the substitution across sources of imports could have on the volatility of domestic and world prices. The model that is presented here includes that dimension and we havemade a final exercise where we try to analyse how the model behaves under different elasticities of substitution between domestic product and imports at ROW. Since in our framework we havemodelled HOME as a pure exporter, only will be changed the elasticity of substitution for the ROWsimports. Again, we have made two sets of simulations, one for shocks coming from HOME and onefor shocks coming from ROW.

The elasticity of substitution will play a central role in the domestic and in the international volatility.If consumers perceive the domestic and the imported goods as highly substitutable, it is expected thatthe evolution of the domestic price and the international price will be similar. Since consumers do notconsider the price volatility in their decisions, they will substitute away from the more expensivedomestic product, for example, to the cheaper import. As a consequence, that substitution willexercise a pressure in the domestic market that will bring the prices down. If the consumer cannoteasily substitute one product for the other, it is expected that the volatility will be higher since thedemand only adjusts through the domestic market


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When the shock is coming from ROW and we increase the elasticity of substitution, we see differentbehaviours according to the commodity considered (Table 9). In the case of wheat, we see that thevolatility of the domestic price at ROW is reduced when the elasticity of substitution is increased.However, at HOME, the volatility seems to increase at very low values of the elasticity of substitutionbut it tends to decrease as we continue increasing its value, describing an inverted U. In the case of the international price, the higher is the elasticity of substitution at HOME; the lower is the pricevolatility (Table 11). In the case of Soybeans, we see that the volatility of the domestic price atHOME and at ROW is increased when the coefficient of substitution is increased; and in the case of Maize, both volatilities are reduced when the coefficient of substitution is increased. As aconsequence, there seem to be different behaviour in the domestic price according to the commodityconsidered.

Table 9. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of the elasticity of substitution at ROW when shocks are generated in ROW



sigmaq09row 0.136 1.970 0.028 1.6962 0.977 2.243

sigmaq11row 0.198 1.924 0.026 1.6976 0.637 2.207

sigmaq12row 0.228 1.914 0.025 1.6984 0.450 2.164

sigmaq13row 0.242 1.906 0.025 1.6992 0.359 2.120

sigmaq14row 0.250 1.900 0.024 1.7000 0.353 2.083

sigmaq15row 0.253 1.894 0.024 1.7008 0.374 2.055

sigmaq20row 0.250 1.873 0.025 1.7045 0.397 1.984

sigmaq30row 0.227 1.847 0.029 1.7099 0.375 1.933

sigmaq40row 0.204 1.831 0.033 1.7135 0.357 1.904

sigmaq80row 0.150 1.804 0.040 1.7204 0.286 1.842

sigmaq160row 0.114 1.789 0.046 1.7246 0.208 1.802

sigmaq320row 0.096 1.782 0.050 1.7269 0.157 1.781

Table 10. Coefficient of variation of the domestic price at HOME and ROW under differentvalues of the elasticity of substitution at ROW when shocks are generated in HOME



sigmaq09row 1.824 0.044 1.658 0.2188 2.074 0.116

sigmaq11row 1.824 0.039 1.655 0.2011 2.072 0.094

sigmaq12row 1.824 0.037 1.654 0.1953 2.074 0.087

sigmaq13row 1.824 0.035 1.654 0.1907 2.075 0.081

sigmaq14row 1.824 0.034 1.654 0.1871 2.077 0.076

sigmaq15row 1.824 0.033 1.653 0.1841 2.078 0.072

sigmaq20row 1.824 0.030 1.653 0.1748 2.084 0.059

sigmaq30row 1.825 0.027 1.652 0.1675 2.089 0.049

sigmaq40row 1.825 0.026 1.652 0.1645 2.092 0.045

sigmaq80row 1.826 0.025 1.652 0.1608 2.097 0.041

sigmaq160row 1.826 0.024 1.652 0.1593 2.099 0.040

sigmaq320row 1.826 0.024 1.652 0.1586 2.100 0.039


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Table 11. Coefficient of variation of the international price under shocks at ROW and atHOME and different values of the elasticity of substitution between domestic and importedproducts

ROW SHOCK HOME SHOCK


sigmaq09r 6.59 2.01 28.09 sigmaq09h 0.78 2.20 3.54

sigmaq11r 3.58 1.95 22.24 sigmaq11h 0.57 1.70 2.36

sigmaq12r 2.98 1.93 18.58 sigmaq12h 0.50 1.53 2.01

sigmaq13r 2.59 1.91 15.16 sigmaq13h 0.45 1.39 1.73

sigmaq14r 2.35 1.89 12.26 sigmaq14h 0.40 1.28 1.52

sigmaq15r 2.19 1.88 9.97 sigmaq15h 0.37 1.19 1.34

sigmaq20r 1.88 1.83 4.23 sigmaq20h 0.26 0.89 0.84

sigmaq30r 1.76 1.79 2.05 sigmaq30h 0.17 0.62 0.49

sigmaq40r 1.72 1.77 1.80 sigmaq40h 0.13 0.50 0.35

sigmaq80r 1.69 1.75 1.67 sigmaq80h 0.07 0.32 0.18

sigmaq160r 1.70 1.74 1.64 sigmaq160h 0.05 0.24 0.11

sigmaq320r 1.72 1.73 1.66 sigmaq320h 0.04 0.20 0.07

When the shock comes from HOME, we see a reduction in the volatility of the domestic price atROW in all cases (Table 10). Again, being consumers able to substitute domestic by importedproducts help to stabilise the price at ROW. However, the response at HOME depends on the productconsidered. In the case of wheat, we see a marginal increase in the coefficient of variation at the ROWis more able to substitute products. In the case of soybeans, the volatility is marginally reduced as theelasticity of substitution at HOME is increased. In the case of maize, on the other hand, the volatilityof the domestic price at HOME is increased when the ROW substitutes more easily domestic andimported products. Finally, from Table 11 we see that the higher is the elasticity of substitution

between domestic and imported products at ROW; the lower is the volatility of the World price.

As a consequence, the more flexible are consumers in terms of their preferences for the domestic andthe imported good, the less volatile is the domestic price at ROW and the international price. The onlyexception is again, soybeans, where HOME is an important supplier but also an important consumer.However, at HOME the volatility varies according to the commodity analysed. In the case of maizethe volatility tends to increase when the shock comes from HOME and decrease when the shock comes from ROW. This implies that HOME cannot send to the World market the internal volatilitybut also it will not receive the volatility generated abroad. The fact that the volatility of the worldprice is reduced when consumers at ROW are more flexible in their demand decisions does not seemto help to stabilise the domestic price at HOME.

These results are very sensitive to the demand structure chosen for ROW. When the shock isgenerated, the extra exports supplied by ROW can only be absorbed by the domestic market at ROW(through their imports). As a consequence, the ROWs exports have an additional destabilisationfactor in the domestic market at ROW, not present at HOME. If there is a shock at HOME, on thecontrary, and the elasticity of substitution at ROW is high, HOME can easily reallocate the extrasupply in ROWs domestic market.

Finally, the ambiguous domestic volatility effects at HOME require a better understanding of thebehaviour of the model. We have seen that the volatility of the World price is reduced when theelasticity of substitution is increased; however, the volatility in the domestic price at HOME has not avery clear pattern. The results seem to depend on the characteristics of the commodity. However, theunambiguous reduction in the volatility in the World price as the elasticity of substitution is increased,as the theory and intuition suggests, presents an interesting dimension to analyse that could present


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important policy and practical consequences. Again, this requires further analysis and research that itis expected to be covered in the future.

Final comments

From very simple assumptions, this paper developed a model to analyse the behaviour and volatilitycommodity prices produced in multiple countries and when countries are allowed to trade. As aconsequence, this model includes a dimension that had not been extensively or explicitly coveredbefore.

Using real commodity data, it was possible to simulate the behaviour of the model when keyparameters change. In particular, the situation of a pure exporter country was analysed. In theseexercises, it was made a distinction between the origin of the shock (local or foreign) and threedifferent commodities were analysed. The commodities analysed allowed to considered differentsupply conditions for this exporter country.

The addition of the international trade dimension complicates the analysis and the conclusions found

before by other authors seem to be altered. From the local perspective, there is now a clear distinctionto make in terms of the origin of shock since the volatility of the domestic price differs if the shocksare locally or foreign generated. On the other hand, the model behaves different in terms of thecommodity analysed. It is not irrelevant the relative position of the considered country in terms of itsshare of exports. In this sense, it is important to make the distinction between a relevant exportercountry in the World of a commodity and a commodity that is largely exported by some country. Thefact that the results depend on the commodity and particularly, on the supply and demandcharacteristic of each them, calls for interesting empirical applications.

However, it could be seen that when the Rest of the World is flexible in terms of their preferencesbetween domestic and imported goods, the volatility of the domestic prices in the Rest of the Worldand the world price is reduced. However, the volatility of the domestic price in the exporter countrydepends on the commodity considered. Despite this results being sensitive on the way the demand inthe rest of the world has been modelled, it presents interesting characteristics to analyse respect tohow the volatility is transferred between countries and could call for interesting policy dimensions.

This paper could not explain the conditions under why these effects occur. The analytical solution,given the non-linearity of the model, impedes it. However, it opens the door for a following researchthat is undergoing indeed. Moreover, the results presented here could be significantly influenced bythe inclusion of storage, futures markets and the Government action. This is also another avenue of research that departs from this first paper.


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References

Armington, P. (1969). A Theory of Demand for Products Distinguished by Place of Production. ATheory of Demand for Products Distinguished by Place of Production , XVI , 159-178.

Bourguignon, F., & Sylvie Lambert, A. S.-E. (2004). Trade exposure and income volatilty in cash-crop exporting countries. European Review of Agricultural Economics , 31 (3), 369-387.

Danthine, J.-P. (1978). Information, Futures Prices, and Stabilizing Speculation. Journal of EconomicTheory , 17 , 79-98.

Deaton, A., & Laroque, G. (1996). Competitive Storage and Commodity Price Dynamics. The Journal of Political Economy , 104 (5), 896-923.

Deaton, A., & Laroque, G. (1992). On the Behaviour of Commodity Prices. The Review of EconomicStudies , 59 (1), 1-23.

Dervis, K., de Melo, J., & Robinson, S. (1982). General Equilibrium Models for Development Policy. Cambridge: Cambridge University Press.

Devarajan, S., Lewis, D. J., & Robinson, S. (1993). External Shocks, Purchasing Power Parity, andthe Equilibrium Real Exchange Rate. The World Bank Economic Review , 7 (1), 45-63.

Hirshleifer, D. (1990). Hedging Pressure and Futures Price Movements in a General EquilibriumModel. Econometrica , 58 (2), 411-428.

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Newbery, D. M., & Stiglitz, J. E. (1979). The Theory of Commodity Price Stabilisation Rules:Welfare Impacts and Supply Responses. The Economic Journal , 89 (356), 799-817.

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Turnovsky, S. J. (1983). The Determination of Spot and Futures Prices with Storable Commodities. Econometrica , 51 (5), 1363-1387.

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ANNEX I

Expected profit and variance

The expected profit can be calculated as

= = + 12 = , + 12 The conditional variance of the profit is

, 1= , 1= + 12 , + 12 = +2 2, 2 +2, 2 + , +2, +

Where, for simplicity, we have replaced = , 1= +2 ,+2, 2, 2 ,+ 2, 2+ , +2, + Now, given that

= , 1 , And= , 1 = , 1 Then, the expression can be reduced after making the correspondent replacements and substitutions in

, 1= , 1+2 , + , 1


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ANNEX II

Elasticity of demand

There are two sets of simulations. Those named betaXXhom analyse how the model behaves undershocks given to the HOME output under different elasticities of demand at HOME. Those scenarioslabelled betaXXrow analyse how the model behaves under shocks given to the ROW output underdifferent demand elasticities at home

ShocksHOME ROW

WHEAT +25% of output (+0.36) in year 5 +25% of output (+15.35) in year 5SOYBEANS +25% of output (+1.18) in year 5 +25% of output (+4.186) in year 5MAIZE +25% of output (+0.54) in year 5 +25% of output (+17.27) in year 5

Beta values HOME ROWbeta06hom/row 0.6 3beta07hom/row 0.7 3beta08hom /row 0.8 3beta09HOM /row 0.9 3beta10HOM /row 1 3beta11HOM /row 1.1 3beta12HOM/row 1.2 3beta13HOM/row 1.3 3beta14HOM /row 1.4 3beta15HOM /row 1.5 3beta20HOM/row 2 3beta30HOM /row 3 3

beta40HOM/row 4 3beta50HOM/row 5 3beta60HOM/row 6 3beta120HOM/row 12 3beta240HOM /row 24 3

Coefficient of risk aversion= 1Armington elasticity (sigmaq)=2

Elasticity of substitution between domestic product and imports

There are two sets of simulations. Those named sigmaXXh analise how the model reacts underdifferent Armington elasticities under shocks generated at HOME. Those shocks labelled sigmaXXrlooks into how the model behaves under different Armington elasticities when the model is shock inthe ROW.

ShocksHOME ROW

WHEAT +25% of output (+0.36) in year 5 +25% of output (+15.35) in year 5SOYBEANS +25% of output (+1.18) in year 5 +25% of output (+4.186) in year 5MAIZE +25% of output (+0.54) in year 5 +25% of output (+17.27) in year 5


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Sigmaq values

ROW HOMEsigmaq09h 0.9 N/Asigmaq11h 1.1 N/Asigmaq12h 1.2 N/A

sigmaq13h 1.3 N/Asigmaq14h 1.4 N/Asigmaq15h 1.5 N/Asigmaq20h/r 2 N/Asigmaq30h/r 3 N/Asigmaq40h/r 4 N/Asigmaq80h/r 8 N/Asigmaq160h/r 16 N/Asigmaq320h/r 32 N/A

Coefficient of risk aversion

There are two sets of simulations. Scenarios name craXXr analyse how the model behaves underdifferent values of the coefficient of risk aversion when the shock comes from HOME. Scenariosnamed cra XXh analyse it when the shock comes from HOME. For some reason, the model could notbe solved at the same time for the three commodities. As a consequence, there are separate files forthe simulations on wheat and the simulations on soybeans and maize.

HOME ROWWHEAT +25% of output (+0.36) in year 5 +25% of output (+15.35) in year 5SOYBEANS +25% of output (+1.18) in year 5 +25% of output (+4.186) in year 5MAIZE +25% of output (+0.54) in year 5 +25% of output (+17.27) in year 5

Sigmaq values

ROW HOMEcra_04h/r 1 -0.4cra_03h/r 1 -0.3cra_02h/r 1 -0.2cra_01h/r 1 -0.1cra01h/r 1 0.1cra02h/r 1 0.2cra03h/r 1 0.3cra04h/r 1 0.4cra05h/r 1 0.5cra06h/r 1 0.6cra07h/r 1 0.7cra08h/r 1 0.8cra09h /r 1 0.9

cra10h/r 1 1cra11h/r 1 1.1cra12h/r 1 1.2cra13h/r 1 1.3cra14h/r 1 1.4cra15h/r 1 1.5cra20h/r 1 2cra30h/r 1 3cra60h/r 1 6cra120h/r 1 12

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