metadata: authors: 0: author: Arroyo Marioli,Francisco
count: United States
docna: 0: docna: Trading Places : Fundamentals, Speculation,
            and Information in US Corn Markets
docty: Policy Research Working Paper
abstracts: cdata!: What explains the surge and plunge
            commodity markets have undergone in the past 20 years? Are
            speculators to be blamed? Do prices reflect full
            information? These are the main questions addressed in this
            paper, in the context of the corn market. This paper
            formulates and calibrates two quantitative models of corn
            prices formation. The first model is designed to explain
            prices in the long run (annual frequency), while the second
            model applies to prices in the short run (quarterly
            frequency). For the long-run analysis, the paper finds that
            deviations of theoretical prices from observed ones are very
            small after 1996, and before 1996 they can be explained by
            government intervention. For the short-run analysis, the
            model is designed to mimic the typical seasonality seen in
            agricultural markets, incorporate supply and demand shocks
            as well as news shocks, and allows for speculative storage
            decisions. The paper finds that demand and supply
            fundamentals can account for around 52 percent of past price
            changes from 1975 to 2016. The model also estimates the
            impact of information shocks to explain an additional 18
            percent of quarterly deviations. Finally, it finds that at
            least 30 percent of short-run price changes seem to have
            explanations other than supply or demand fundamentals or
            information, demonstrating that when analyzing quarterly
            data, prices do not always closely track fundamentals.
display_title: Trading Places : Fundamentals,
            Speculation, and Information in US Corn Markets
listing_relative_url: /research/2023/07/34127115/trading-places-fundamentals-speculation-information-corn-markets
topicv3: Food Price Analysis m1326440 200,Agricultural Output Markets m1327136 1965,Commodity and Resource Prices m1503849 3034
publishtoextweb_dt: 2023-07-31T00:00:00Z
dois: 10.1596/1813-9450-10531
origu: Off of Sr VP Dev Econ/Chief Econ (DECVP)
author_keys: 0: author_key: 1853050
model_extractions: Policy Research Working Paper 10531

# Trading Places

Fundamentals, Speculation, and Information in US Corn Markets _Francisco Arroyo Marioli_ Development Economics Prospects Group July 2023
Policy Research Working Paper 10531

# **Abstract**

What explains the surge and plunge commodity markets have undergone in the past 20 years? Are speculators to be blamed? Do prices reflect full information? These are the main questions addressed in this paper, in the context of the corn market. This paper formulates and calibrates two quantitative models of corn prices formation. The first model is designed to explain prices in the long run (annual frequency), while the second model applies to prices in the short run (quarterly frequency). For the long-run analysis, the paper finds that deviations of theoretical prices from observed ones are very small after 1996, and before 1996 they can be explained by government intervention. For the short-run analysis, the model is designed to mimic the typical seasonality seen in agricultural markets, incorporate supply and demand shocks as well as news shocks, and allows for speculative storage decisions. The paper finds that demand and supply fundamentals can account for around 52 percent of past price changes from 1975 to 2016. The model also estimates the impact of information shocks to explain an additional 18 percent of quarterly deviations. Finally, it finds that at least 30 percent of short-run price changes seem to have explanations other than supply or demand fundamentals or information, demonstrating that when analyzing quarterly data, prices do not always closely track fundamentals.

This paper is a product of the Prospects Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at farroyomarioli@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Trading Places: Fundamentals, Speculation, and Information in US Corn Markets Francisco Arroyo Marioli Key words: Information Acquisition, Market E¢ ciency, Commodities, Agricultural Demand, Agricultural Productivity JEL codes: G14, Q02, Q11
# 1 Introduction

The objective of this paper is to study the fundamental and non fundamental determinants of commodity prices over the past decades. The analysis speci...cally focuses on corn markets, for several reasons. Corn and soybeans are the main agricultural commodities in terms of production market value. They are the most traded contracts in futures market (next to cotton and wheat). Also, the US is the world leader in corn production, consumption and exports. It plays a signi...cant role in several states and sectors of the US economy, to the point where it has been considered a strategic sector for the US government for a long time. Prior to 1995, the US federal government would regularly intervene in these markets, usually seeking to guarantee minimum prices for producers by buying production. In more recent years, the government has shifted its intervention towards the demand side by incorporating biofuel mandates instead. Either policy signals this sector’s importance to policymakers even until today.

This paper compares prices de...ned by fundamentals versus observed prices. It de...nes fundamental determinants of price as demand and supply shocks. These may be either current or future. Future demand and supply shocks a¤ect current prices through information shocks (agents acknowledge that shocks will occur in the future) that change current inventory holding decisions. This paper is divided into two parts. The ...rst part studies the current determinants of corn prices at an annual frequency, while the second part studies the short-run, cyclical determinants. The ...rst section determines how annual prices would have changed solely based on current demand and supply shocks. The reason for this is simplicity: the paper shows that even when focusing only on current shocks, the model ...ts the data very well. Any additional feature would only increase the performance of the model, thus making my results only stronger. The second part constructs theoretical prices at a quarterly frequency. Given that supply is zero in some quarters, the model introduces inventory purchases as part of the market. Given that inventory purchases are made within a pro...t maximizing scheme, expectations, and therefore future shocks through information, start playing a key role. The paper hence introduces in this section future shocks as part of fundamental-determined prices.

More speci...cally, in the annual model, the paper analyzes the long-run price trend from 1975 to 2015. It then simulates a theoretical price time series, de...ned as the price such that each 3
year’s demand matches supply or, in other words, a price such that inventory variations are zero. Moreover, it is even possible to assume that inventories could reach zero at the end of the year, given that, in practice, in the last quarter it usually reaches very low values with respect to harvest size. It proceeds to compare these theoretical prices with observed ones and estimate the di¤erence, and ...nd that after 1996, di¤erences are small and do not last more than a year or two. Additionally, this document ...nds that the increase in price levels in the 2000s seems to be explained mostly by the presence of an increasing demand for bioethanol.

In the quarterly model, it follows a market structure that mimics the typical seasonality seen in agriculture markets ( with production occurring only during one quarter). Given that the time lapse between decisions is shorter, it also allows for information shocks to occur by introducing them to the agent’s expectations through private and public signals. Results show that around 70% of price volatility can be explained through the shocks cited above, leaving a 30% measured space for other non fundamental sources of variation.

Regarding model speci...cs, the long run case assumes isoelastic forms Dt = Ztp<sup>�</sup> t<sup>fordemand</sup> and St = Atp<sup>�</sup> t<sup>forsupply,the...rsttermrepresents(exogenous)levelsandthesecondtermthe</sup> endogenous response to price with the respective elasticity. Therefore, shocks are captured as changes in Zt; At. These will be de...ned as the current fundamental source of price changes. Time series for these variables can be obtained using USDA corn usage and production data. They are then integrated into a market clearing equation with no storage decisions. The short run case considers demand as a whole aggregate and assume identical isoelastic functions for both demand and supply, as before. The model is linearized, calibrated and simulated with real shocks as inputs. It then estimates the impact of di¤erent shocks (demand, supply, and information) on price changes and quanti...es them.

One additional analysis that results from this paper is related to the issue of prices’being fully informative and appropriate for business-cycle measurement. Romer (2006) raises this question and shows evidence of ...rms that do not always behave in pro...t-maximing ways by analyzing the case for professional football teams. This paper shows that although in the long run, prices seem to be very close to fundamentals, when going to a quarterly frequency, market prices can sometimes be very far away— as much as 50%— from them. These results are in line with Hussman (1992), who shows that once imprecise signals are introduced in a rational expectations framework, market prices become 4
ine¢ cient in transmitting information. Because corn markets are considered to be well-functioning markets, in the sense that prices and transactions are transparent, centralized, and very liquid, it is surprising and interesting to ...nd that they might not always behave as one would expect in a classical supply-demand model with inventories and utility and pro...t-maximizing agents. This raises several relevant questions regarding macroeconomics, ...nancial markets and industrial organization. First, if a very well developed market fails to deliver fully informative prices, what can then be said regarding other markets, where illiquidity, information asymmetry and search costs are more relevant? Moreover, since these results are found for quarterly data, the implications for business-cycle accounting could be important. In several developing countries commodity markets such as corn have a signi...cant impact on overall GDP and exports. If the prices that are being used for measurement are not market-clearing ones, important distortions could be taking place. Also, since annual prices do not di¤er from fundamentals as much as quarterly ones do, another potential question arises: Should we produce national accounts using prices measured at quarterly, annual, or some other frequency? How much time do markets need to become fully informative? Many business-cycle theorists believe that shocks on the real side of the economy, such as shocks to TFP and commodity prices, trigger and propagate economic ‡uctuations. Commodity price shocks clearly play important roles in developing nations today, particularly resource exporters and have also played a large role in economic ‡uctuations in the past. Economists and policy makers believed, for example, that the commodity-price declines in the late 1920s and early 1930s contributed to the length and severity of the Great Depression. In 1933, the Roosevelt administration’s e¤orts to raise commodity prices, particularly prices of farm products like corn, formed the centerpiece of its e¤orts to resurrect the economy. These results have implications for the sources of shocks and the accuracy of the interpretation of the shocks derived from RBC models. Given that productivity is a key driver of the cycle, a price system that does not track fundamentals closely could result in ine¢ cient resource allocations, or in other words, aggregate productivity losses. Therefore the implications of these ...ndings are relevant regarding short-term business cycles. In the short run (at business-cycle frequencies), the majority of commodity price shocks do not re‡ect supply and demand, but could instead be a¤ected by speculative factors. These distortions could have a signi...cant impact on commodity producing economies.

This paper is divided into four sections. The ...rst section introduces and explains the main 5
structure of the paper and its relationship with the literature. It also applies a standard empirical approach used in the literature for oil markets to corn, to motivate and provide a benchmark for the models. Section 2 presents the low-frequency model and its results. Section 3 presents the high-frequency model, calibration, and estimation results. Section 4 summarizes and concludes.

# 1.1 Literature Review

This paper, therefore, contributes to the literature in three respects: ...rst, it tests the hypothesis that the spike in commodity prices was due to by non fundamental reasons, but focuses on a less explored market, since most of the literature has focused on oil markets. Second, it adds a new feature to high-frequency analysis: information shocks. This paper quanti...es the historical impact of information shocks by incorporating USDA reports as a source of information. Additionally, it estimates private signals and their impact on prices, showing that when it comes to quarterly analysis, they are a relevant source of volatility. Third, it decomposes price changes per source of change— that is, it estimates the impact of each variable change each year, from 1975 to 2015, and therefore o¤ers alternative explanations for the observed change in prices in past years. This also allows to estimate the fraction of prices that cannot be explained by fundamental or information factors, leaving a measured space for further research.

Some papers have already attempted to use competitive models to study these markets. Roberts and Tran (2012) use a competitive model to estimate the role ethanol mandates in corn prices, ...nding they can account for 11 to 0 percent of food price increase between 2005 and 2011. Zhou and Babcock (2017) use a model to estimate the role of hypotheically reducing biofuel mandates on prices. Mallory et al (2012) use this approach to link ethanol and corn markets, ...nding that under certain conditions, future price expectations can in‡uence nearby futures across each other. Tegene et al (1988) make use of this method to estimate long-run price elasticity of corn acreage, ...nding it to be 0.2.

More generally, the literature has also examined whether commodity markets have been altered for non fundamental factors in the past decades, such as ...nancial speculation. For instance, in energy markets results tend to indicate small or null e¤ects of speculation on oil prices. In their canonical paper, Kilian and Murphy (2014) develop a VAR model with speculative demand shocks and contrast it with recent oil inventory data and ...nd no basis for speculation’s being blamed for 6
the 2003-2008 price period. They do, however, ...nd it plausible that there was some in‡uence in previous years 1979, 1986, and 1990. Knitell and Pyndick (2016) analyze the oil market using a simple static partial equilibrium model with inventory markets and again ...nd no relation between speculation and the oil price peak in 2008. Fattouh, Kilian, and Mahadeva (2013) summarize the literature that examines oil markets and conclude that there is no evidence that speculation is the main driver of price increases. Baumister and Hamilton (2019) also test a VAR approach for oil market but introducing priors for elasticities, ...nding that supply disruptions tend to be a much bigger factor than in previous research.

Another branch analyzes commodity ...nancial markets from a portfolio point of view. Bohl and Stephan (2012) study the e¤ect of increased trading in future markets for six top traded agriculture and energy commodities using a GARCH model approach and ...nd no evidence of a causal relation between future trading and price volatility. Chary, Lochstoer, and Ramadorai (2013) show that restrictions in ...nancial markets can alter spot prices through hedging decisions, a¤ecting real outcomes. Sockin and Xiong (2015) study the possibility of information frictions in commodity markets, and demonstrate the importance of prices as signals for both demand and supply and the weakness of assuming that shocks are publicly known. In line with their results, this paper incorporates information shocks and allows for some shocks to be unknown.

The work presented in this paper is mostly related to Knitell and Pyndick (2016), who estimate non fundamental shocks as deviations in inventory levels. The paper follows a similar methodology except that it consider corn markets (instead of oil) and a dynamic framework (rather than static).

# 1.2 A preliminary analysis

Empirical models have been used extensively in the commodity’s literature, though mostly for energy and metals. Given the lack of similar approaches used for corn, this section explores the use of these same techniques in corn markets The goal is to motivate the theoretical models used in this paper.

The estimation proceeds to construct a VAR model with sign restrictions based on Kilian and Murphy’s (2014) model for oil. The endogenous variables are the same ones to be used later in the theoretical models: real price, consumption, production, and storage. Real prices, consumption, 7
and production are taken in log-di¤erences. Stocks are normalized as a fraction of same-year consumption. Sign restrictions follow Kilian and Murphy’s (2014) assumptions when applied to the same shocks: a positive supply shock increases consumption and production, while reducing prices; a positive demand shock increase prices as well as consumption and production; a positive speculative shock increases inventories, prices, and production, while decreasing consumption. The estimation uses annual data due to the extreme seasonality of corn production (three quarters of the year will always produce literally zero), and therefore add only one lag to model.

Results can be seen in ...gure I. The ...gure shows the historical decomposition of price changes by shock. The ...gure is quite indicative of the role of demand shocks: they clearly seem to play the biggest role, explaining 34 percent of price variation between 1981 and 2015. Speculative shocks explain 28 percent while supply explains 19 percent. This result holds some similarites to Kilian and Murphy’s (2014) model for oil, where they ...nd that demand shocks are the biggest player in the long run, though in their case it is much more absolute almost 87 percent of the long-run real price ‡uctuations are due to demand. There are certain limitation though to this result. As the Kilian and Murphy mention in their 2014 paper: "Impact sign restrictions alone are typically too weak to be informative about the e¤ects of oil demand and oil supply shocks". Therefore, the next sections proceed to use theoretical approaches so to better identify the actual sources of corn price changes.

8
<!-- Start of picture text --> O.4<br>03 Pe 4<br>fe . |<br>oe hi | Nit‘ rl | li4 kSir<br>q See) }<br>MANGA:§ EL| JUNin :eelh.: BR BDA EME| ~ oleTUL ELRS |] NatyN ‘A<br>HVmma NS VAN US ciao S|! Ni)||<br>01 VON oo RS a ! io MUR<br>4 NV i] \ \ \ a<br>0.2 I 3<br>| i! Jil<br>I Hl H | , |<br>-0.3 Nn ul i<br>U H<br>“04 Hn<br>f=sDemand i!<br>O05 ASSSS Upply<br>Ips peculative<br>-0.6 mm Residual<br>ol otal<br>-O.7<br>1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
fundamentals because of the presence of non fundamental factors, such as, due to the growing importance of ...nancial speculation. This section proposes the following experiment: Calculate the theoretical price that would balance supply and demand every year and compare it with the observed price. That is, calculate the price such that inventory variation would have been zero. The intention behind this simple experiment is to see how prices would have changed solely based on current demand and supply shocks.Any additional features added here would only enhance the results, therefore the ...t that will be shown can only be enhanced but not worsened by any additional feature of analysis we might want to add. This sections shows that even under this simple framework, results are very conclusive. It also implies an more long-run based approach. In the long-run, inventories cannot play a signi...cant role in price determination. Under the plausible assumption that speculators do not seek to buy-and-hold inventory, it is clear that in the long run prices cannot deviate far from fundamental ones. To understand this better, assume it is not the case. That is, assume that the fundamental price is systematically below or above equilibria with no inventory change. This would imply that stocks either decrease every year or accumulate in...nitely. Neither scenario is consistent with long-run equilibria, since it would either imply hitting the zero lower bound or an irrational accumulation of stocks. Since the analysis is long-run based this can be a useful approach.

Formally, the theoretical price results from the following market-clearing equation: The left-hand side of the equation is demand for corn, and has four subcomponents: ethanol, food industry, feed (and residual) and exports. Supply has only one source: farming. Imports in the US are (practically) zero. For simplicity, demand and supply are assumed to have isoelastic functions of the price, as in Knitell and Pyndick (2016) and similar to Deaton and Laroque (1996). In this model, for demand functions, Zt; captures exogenous demand shocks and p<sup>�</sup> t<sup>!</sup> the endogenous response to prices, with ! being the demand elasticity parameter. For supply, At represents 10
productivity and � supply elasticity.

<u>1 Zt</u> !+� Equation (1) thus de...nes the theoretical market price as p<sup>�</sup> t<sup>=</sup> h At i . Also, to quantify the impact of di¤erent shocks, one can calculate the ...rst-order e¤ect for each of them.

where the right-hand side gives us the sum of the e¤ect of changes in all i 2 ffood,feed,ethanol,exportsg demand fundamentals and production fundamental A: USDA databases have time series for prices, all four demand uses (ethanol, feed, food, and exports), production, and yield per acre. The model uses these to estimate elasticities and identify exogenous shocks. For demand price elasticities, it uses instrumental variables, taking yield per acre shocks as a ...rst-stage instrument for prices. Changes in yield per acre are explain mostly by weather factors. Farmers have almost no control over short run productivity levels. Therefore, it is reasonable to assume that they are exogenous to the production process and are appropriate instruments for prices. Supply elasticities are estimated following Roberts & Shlenker (2013). Estimation results can been seen in Table I.A. Results fall within other literature’s ...ndings<sup>1</sup> . Once elasticities are estimated, given demand, supply and price data, one can identify exogenous components by reversing the isoelastic equation and setting the exogenous component equal to the demand or supply level times prices elevated to inverse elasticity.

Given time series for At; Zt<sup>i;andpt;andestimatedvaluesfor!; �,onecandecomposeprice</sup> changes per year by estimating the di¤erent terms of equation (2). As a result, changes in inventories explain the remaining residual. Results per variable can be seen in Figures II to V.

> 1 The Food and Agriculture Policy Institute shows elasticity estimations for corn in di¤erent countries, giving results that are always between 0.1 and 0.5. for both demand and supply. http://www.fapri.iastate.edu/tools/elasticity.aspx

11
The next step is to solve for the price equation (1) from 1981 to 2015. Figure II.A shows the theoretical price that results from the simulation and compares it against observed prices. The ...gure suggests two key observations: First, di¤erences between the model-based and observed price are much larger before 1996 than after. That year, a more market-friendly US agriculture policy bill was passed, which reduced the budget for government purchases (hence the scope for intervention) and lowered price ‡oor targets below market equilibria. It is clear that after such an event, the distance between both time series reduces heavily. Regarding the 2000s spike in prices, the hypothesis of a non-fundamental driver seems pretty weak, since prices moved as one would expect them given demand and supply shocks. Second, theoretical volatility reduces signi...cantly after the year 1996.

Table I.A

|Description|Parameter|Value|
|---|---|---|
|Demand Elasticity|!|0:18<sup>���</sup>|
|Supply Elasticity|�|0:15<sup>���</sup>|

Table I. *,**, and *** indicate p-values inferior to 0.1, 0.05, and 0.01, respectively: Table I.B

|||Standard Deviation|
|---|---|---|
|Variable|All|Prior to 1996<br>After 1996|
|Observed Price (in logs)|0:39|0:36<br>0:32|
|Fundamental Price (in logs)|0:59|0:74<br>0:36|
|Observed to Fundamental Ratio|0:41|0:59<br>0:12|
|||Correlation|
|Observed vs Fundamental Prices|0:82|0:72<br>0:96|

Table I.B.The ...rst two rows show standard deviations of both observed and fundamental prices for each time interval. The row "Observed to Fundamental Ratio" indicates the standard deviation of the ratio of observed prices divided by fundamental ones. The ...nal row "Observed vs Fundamental Prices" shows the correlation between observed and fundamental prices for each time interval. A traditional statistical F test 12
<!-- Start of picture text --> 6<br>| — Observed<br>5 \ — — — - Theoretical<br>/<br>I) 1996 Farm Bill<br>|<br>4||<br>||<br>|<br>|<br>3 | | I<br>i h<br>|<br>|<br>i! 1<br>2 ; 1|1 ;<br>yb I || ,<br>I | | | 4 ", at<br>| s o my ! \ - v<br>é / a f<br>1 ce 1 ho! -<br>0<br>1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
changing both supply and demand elasticities to values between 0.05 and 0.25 will change the total fraction of price changes induced by supply to be between 58 and 62 percent.

In 1996, a Farm bill was passed. It signi...cantly shifted U.S. farming policy from a highly interventionist one toward a more "free market" approach. Prior to this bill, U.S. farming policy was heavily biased toward sustaining minimum price levels set at the discretion of the policymaker. The main tool through which this took place was by either government purchase of goods (The Commodity Credit Corporation - CCC- program) or subsidies to storage in the private sector (Farmer-Owned Grain Reserve program). Figure IV quanti...es the e¤ect these programs had on price levels. After 1996, the government budget allocated for purchasing goods was minimized, and minimum prices were set below market values; this resulting in a practically zero direct government intervention in corn markets. Table I.B shows statistical moments before and after the bill was passed in 1996. Table I.B shows standard deviations for observed prices and fundamental ones, standard deviation of the ratio and correlation. Two important facts emerge. First, the ratio between observed price and "fundamental" ones becomes signi...cantly more stable after 1996. A traditional statistical F test was performed to check for a null hypothesis of equality in standard deviations of the ratio before and after 1996, with results rejecting a null hypothesis at less than 1% signi...cance. This is also in line with an increase in correlation between both series. Second, the volatility of fundamental prices themselves also drop after 1996. This new stability could perhaps be one of the reasons for the lack of direct intervention during those years.

Regarding the 2000s, it is clear that observed prices do not deviate too signi...cantly from fundamental ones. That is, the price that would have theoretically cleared the market with no storage decisions has not deviated signi...cantly from observed prices. This suggests that speculation (or other non fundamental shocks) has had little— if any— e¤ect on market prices.

The immediate question is then: If not speculation, what has drives the price spikes? Apparently, as can be seen in ...gure II.B, ethanol explains almost 56% of the price increase between 2005 and 2010. This can partially be explained by technological improvements (that allow ethanol to be used in energy markets) and government policy that has forced gasoline producers to incorporate mandatory fractions of ethanol in their ...nal products. This decomposition has been calculated by inputting the estimated values of fundamentals and elasticities into equation (2). Additional evidence for this is the increased correlation between oil and corn prices, as in Figure VII (see 14
<!-- Start of picture text --> 0.3<br>i__.! Ethanol Use<br>02 ME Food Use<br>HE Exports<br>0.1<br>_l 7-77<br>-0.4 a.<br>a<br>05<br>1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
1) <!-- Start of picture text --> 0.5<br>0.4<br>0.3<br>0.2<br>0.1<br>0<br>-0.1<br>-0.2<br>-0.3<br>-0.4<br>1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
that are not necessarily related to supply and demand fundamentals. Therefore, though this section continues to assume isoelastic functional forms for supply and demand, it adds speculators as a new type of agent. The justi...cation for this is that given that production of corn occurs only during fall quarter , buying and selling storage inevitably becomes a relevant factor in determining market prices throughout the whole year. That is, give that production only occurs during on quarter, it is unrealistic to ignore inventory changes as a relevant factor. Since in a decentralized framework these inventory decisions are pro...t-seeking, the model rationalizes this by introducing a representative speculator: an agent who makes decisions based on expected pro...ts realized by buying low and selling high. The objective in the next section is to model short-run quarter equilibria and quantify the impact of both current and future shocks (the latter through information shocks) on total variation, similar to what was done in the previous section.

# 3.1 Model

Time has two dimensions: year and quarter. Notation wise, t represents time change from quarter to quarter, q indicates a quarter-speci...c notation, and y represents marketing (not calendar) year. A marketing year starts with the harvest and ends exactly before the next one. For simplicity, demand is considered as a whole (that is, there is no di¤erentiation by use). Just as in the previous model, demand and supply are isoelastic. This seems reasonable, given that the demand elasticities found in the previous section were not so di¤erent across the various sources of demand.

where Zy;t; Ay;t are exogenous random variables representing demand and supply fundamentals and have the following dynamics: 17
Shocks are all IID and have the following distributions: Annual shocks Quarter-speci...c shocks .

In other words, demand shocks have a yearly component that follows an AR(1) process, plus a quarter-speci...c noise. Production only comes during one quarter (harvest season); therefore, it is equivalent to de...ne supply shocks as annual or quarterly. In addition to farmers and consumers, speculators, participate in the market by buying and selling stored goods. They are pro...tmaximizing agents who face the following problem: The function f (xt; �xq; �) represents the cost of deviation from a certain quarterly optimum x�q; that has a speci...c value for each quarter and is known, i.e. it is neither random nor uncertain. Deviating from this optimum implies some cost �; �<sup>II</sup> . The cost in the last quarter is di¤erent because usually inventories are managed at low levels during that time of the year. Therefore, given that agents are closer to hitting the zero lower bound, it is reasonable to assume that cost of deviating from optimum are higher. Intuitively, for some industries, having low inventories 18
— 6 _- BE 5 £6 5 |

— 6 <u>_</u> ~~BE~~ .

> é {5,5 }

7 —p _ —p
As a result, given that parameters and market-clearing conditions are quarter speci...c, equilibrium prices will also be quarter speci...c. That is, their values will vary from quarter to quarter, even in steady state.

# 3.2 Information Structure

Information is key to forming expectations for speculators, and therefore the information structure is a relevant issue in the model. This section constructs it to mimic reality as closely as possible.

Production shocks and annual demand shocks are revealed the quarter after they take place, so agents do not know at present moments what supply and demand are. They use both public and private signals to form expectations regarding these. Private signals are formed each quarter. Public signals, on the other hand, are realized only in quarters 1 and 4. The model incorporates public signals this way in order to map USDA reports; hence, it must mimic the same timing schedule. Private signals are private in the sense that they are developed by the private sector. They are observable to speculators, but not to the econometrician.

Information regarding demand and supply fundamentals is only revealed after each quarter is ...nished. During each quarter, therefore the agent does not know with precision what is driving price changes. As an example, in quarter 1, yield, annual demand, and quarter-speci...c demand shocks are realized, but the agent only knows them after the quarter is over. Therefore, in quarter 2 the annual component of demand is known, but not the quarter-speci...c one for quarter 2, and so on.

Uncertainty about current shocks takes place only in quarter 1, since in quarters 2 ,3 and 4 they only speculate with respect to next years fundamentals (which by de...nition have not taken place yet). So, in quarter 1, speculators can observe the current price, but since the current price will depend on the realization of three shocks (annual supply shock, annual demand shock and quarter 1 speci...c demand shock), they cannot identify or map back to fundamentals (there is no 1 to 1 mapping possible). The assumption used here is that if there is any information that can be captured from this it is negligible and for simplicity will be disregarded.

Agents have access to public reports that are issued in the ...rst and last quarters of the marketing year. The ...rst-quarter report predicts current annual demand and yield and the latter predicts the upcoming year’s amounts. Private forecasts regarding next year’s yield and demand, on the 20
|Quarter|Harvest|Annual DemandShock Public Demand Signal|Public Supply Signal|Productivity|Revealing<br>DemandRevealing|
|---|---|---|---|---|---|
||E.A<br>¥|eZ<br>@#Pu<br>¥<br>t|@APu<br>t|||
|1<br>|Xx<br>|x<br>x<br><br>|x<br>|-<br>|-<br><br>|
|2|-|-<br>-|-|xX|X|
|4|-|-<br>X|X|-|-|

~~0”~~ 0” 0” 0” ~~0”~~ 0” 0” 0”
where �<sup>pu;A</sup> t ; �<sup>pu;Z</sup> t ; �<sup>pr;A</sup> t ; �<sup>pr;Z</sup> t are IID noise components and have a normal distribution with standard deviations (or inverse precision) �<sup>�pu</sup> A<sup>; �</sup> Z<sup>�pu; ��pr</sup> A<sup>; ��pr</sup> Z<sup>.</sup> All signals are summarized into the vector �y;t = n�<sup>Apr</sup> y;t<sup>; �Zpr</sup> y;t<sup>; �Apu</sup> y;t<sup>; �Zpu</sup> y;t o The predicted variable will vary depending on the quarter. In harvest quarters, signals predict the annual demand shock and annual supply shock, which are taking place currently. In nonharvest quarters, signal predict next year’s annual demand shock and annual supply shock. This can be seen more clearly in Table III. Therefore, each quarter there will be several sources of shocks: annual demand shocks, annual productivity shocks, quarter-speci...c demand shocks, and public and private information shocks regarding both demand and supply.

|||Table III|
|---|---|---|
|||Predicted variable|
||Harvest Quarter|Non-Harvest Quarters|
|Signal|Quarter 1|Quarter 2<br>Quarter 3<br>Quarter 4|
|�<sup>Apu</sup><br>y;t|"<sup>A</sup><br>y|-<br>-<br>"<sup>A</sup><br>y+1|
|�<sup>Zpu</sup><br>y;t|"<sup>Z</sup><br>y|-<br>-<br>"<sup>Z</sup><br>y+1|
|�<sup>Apr</sup><br>y;t|"<sup>A</sup><br>y|"<sup>A</sup><br>y+1<br>"<sup>A</sup><br>y+1<br>"<sup>A</sup><br>y+1|
|�<sup>Zpr</sup><br>y;t|"<sup>Z</sup><br>y|"<sup>Z</sup><br>y+1<br>"<sup>Z</sup><br>y+1<br>"<sup>Z</sup><br>y+1|

Table III.This table shows what variable is being predicted by each signal in each quarter. In the harvest quarter, signals intend to predict current shocks, since these not inmediately observable. In the rest of the year signals intend to predict next year’s shocks.

Once a signal is received, agents use it to update their previous beliefs. That is, they use past private (public) signals and combine them with their latest private (public) signal, constructing a posterior private (public) signal. For example, in quarter 2, the private demand signal the agent receives is the ...rst one that forecasts next year’s fundamentals. In this case she has a ‡at prior, and therefore her posterior will be identical to the signal received. In the third quarter, however, the agent has a previous private demand signal �<sup>Zpr</sup> 2 and receives �<sup>Zpr</sup> 3 : Assuming both signals have equal precision, she weights them optimally by assigning equal weight to both (recall that the noise 22
6 ”) ”) f) GPT pr ”) ~~7~~ ) ~~7~~ ) ~~7~~ ) Pr ~~P~~ r ”) ~~a~~ ) ~~-~~ 6 ~~-~~ 6 ~~a~~ ) orn ~~—o~~ ?" ght ~~e~~ s ght ~~P~~ t a) GS CG.

0 y 6 (-7 )@ a) os Gc.

0 y 6 (-y7 )@ a) os
goPu gOPu Y <u>sore</u> ~~go~~ r ~~5p,~~ <u>opr</u> goPu gOPu Y <u>sore</u> ~~go~~ p <u>SOP</u> ~~ODT~~ Y +7 ) ie) <u>-</u> <u>-</u> _ <u>6 6</u> O) 6 06 O _ ) e) Q Q ie) (O Q 0 ) _ 0 {© -} Q ,O 6 -
De...nition 2 An equilibrium consists of prices py;t(�y;t; 'y;t) such that, given shocks �'y;t; �y;t�, information set �y;t, and initial conditions X0;1; A�1; Z�1, markets clear for all quarters and the speculator’s FOC is satis...ed for all fy; tg Prices will depend not only on the current level of productivity and demand, but also on the level of initial inventories and available signals. Past productivity and demand can in‡uence this by providing information about future realizations of demand and supply, since they follow an AR(1) process. Given this solution, two main issues remain to be addressed: First and most important, the solution is nonlinear, which makes it impossible to ...nd an explicit solution. Second, private signals are non-observable in the data. Therefore the model will be solved by proceeding through the following steps:

# Step 1

Linearize the system around steady-state values. Normalize these to 1, such that index points can be interpreted as being close to percentage changes.

# Step 2

Calibrate parameters using USDA corn market data for 1975-2016.

# Step 3

Estimate seasonality and simulate the model by feeding estimated shocks as inputs, the compare model prices versus data.

# Step 4

Estimate private signals using a Kalman Filter.

# Step 5

Estimate the contribution of each factor to ...nal prices and measure the residual (unexplained fraction of price changes).

25
# 3.2.1 Step 1

The ...rst step is to linearize the model around steady state. Variables are rede...ned in the following way: ^ � � For any variable y; y = y � y where y is the steady-state value of the respective variable and y^ is the linear deviation from it.

Therefore, one must solve for steady-state values. Steady-state estimates are obtained in the following way: First, de...ne a harvest size of one: A� = 1: Then normalize demand for each quarter, such that they all add up to the harvest Next, estimate quarter-speci...c seasonality Z<sup>�</sup> i for demand in the data and normalize it such that they all add up to the harvest size: For inventories, in steady state they should not deviate from x�q since the values for these are picked such that sticking to the target is always optimum. If speculator’s match their target x�q, the marginal inventory cost is zero These are calibrated by taking average inventory levels (relative to harvest size) for each quarter throughout the whole sample. Therefore, the policy function equation from the speculator’s problem will give us the evolution of prices throughout each quarter in steady state: 26
_ -no--p _ pp _ _- pp _ _- pp yo =p p Po ~~C=~~ B65 BE _ 86 BE[ ]) {5,6 }
equations depend on parameters that vary in each quarter, the price solution equation will also vary depending on the quarter.

Conclusion 3 As a result, the linearized new state space will have four price solution equations, one for each quarter: where �<sup>I</sup> i<sup>; �II</sup> i<sup>;�III</sup> i ; �<sup>IV</sup> i are price policy function parameters with i = 1; ::; 8/ for each state variable and q = I; ::; IV for each quarter. Recall that in steady state �i = 0 for all signals �, both private and public.

It is important to remember that the sole role of "last year’s" production and demand is to inform about future production and demand. Therefore, if persistence parameters �A and �Z are equal to zero, �<sup>J</sup> 7<sup>and�J</sup> 8<sup>shouldalsobezeroforallJ:</sup>

# 3.2.2 Step 2

The model uses USDA data series for yield per acre, production, demand (local and exports), prices, and stocks. The section proceeds ...rst by detrending and deseasonalizing them, then normalize their mean so that index points can be read as percentage points. To obtain the exogenous demand component, the model instruments prices with yield per acre to obtain demand elasticity through a typical IV analysis. The next step is to use residuals as estimates for Zy;t; just as in the longrun-trend model. Then, the section estimates the annual component of the residuals to obtain Zy and Zt series. For supply elasticity �, again the model uses Roberts & Shlenker’s (2013) results. As a robustness check, other values for � were used with very similar results.

28
When it comes to reports, one can make use of digitalized USDA forecasts for each marketing year, from 1975 to 2016. These forecasts are for demand and yield per acre. To obtain �<sup>Zpu</sup> t forecasts from demand forecasts, we regress these last ones against forecasted yields, then use the residual as a demand shock estimate. The reason for this is because given that a simple demand forecast contains also an endogenous forecast, since a higher yield would endogenously result in lower prices and higher consumption, one can eliminate this endogenous component of the demand forecast by regressing it against the yield forecast.

This section calibrates the parameters to simulate and show quantitative results. Given the data available (described above), the section proceeds as the following. First, calibrate the parameters necessary to calculate �<sup>q</sup> i<sup>which are �; �I; �II;A;�Z�y;Z�q; !; and �: Demand and supply elasticities are</sup> estimated as indicated in the previous step. The persistence of supply and demand fundamentals are calibrated by estimating AR(1) processes, and volatility is obtained by taking the residual’s standard deviations.

Storage cost parameters �<sup>I</sup> ; �<sup>II</sup> are estimated by choosing values that minimize residuals. That is, the previous set of equations will give theoretical prices as the result for each quarter. The di¤erence between these and observed prices are the residual. Parameters �<sup>I</sup> ; �<sup>II</sup> were calibrated such that the total sum— in absolute values— of the residuals is minimized.

The next step is to calibrate public and private signaling parameters. Regarding public signals, it is important to say that these appear in speci...c days, which are publicly known in advance. That is, at a certain time, information becomes publicly known in a report and markets react almost instantaneously Price changes for those "announcement" days can be seen, and even though private information is always present in markets, it is reasonable that by constraining price changes to the speci...c announcement day isolates public signal’s e¤ect on prices.

The precision of public forecasts is estimated by comparing USDA demand and supply forecasts versus ex post realizations. The most non-straightforward task, however, is to obtain a value for the precision of private signals. The section proceeds to identify them as follows. First, calculate �<sup>I</sup> 4<sup>and �I</sup> 5<sup>by usingthe method of undetermined coe¢cients (also use this to obtain all parameters</sup> �<sup>q</sup> i<sup>).Second,obtainthereleasedatesforpublicsignals(USDAforecastreports)andthesame-day</sup> price reactions. Then, regress same-day price changes against the changes in forecasted values in the released reports— with respect to the previous report— for that day. This allows to estimate the 29
e¤ect of public signals on price changes. The parameter that relates price changes to public supply signaling in the model, �4�1;A;should match this previous price reaction estimation. Once known the value for �4�1;A, and given that also �4;is known one can obtain the value of the weight of �<sup>�pu�1</sup> public signals relative to private ones, �1;A Since �1;A = �<sup>�pu�</sup> 1<sup>1</sup> <u>;yA</u> and public signal precision, 1;y;A<sup>+��pr</sup> 1;y;A<sup>�1</sup> �<sup>�puisknown,onecanidentifyprivatesignalprecision,��prTheproceduretoidentify��pr</sup> A<sup>;</sup> A<sup>.</sup> Z<sup>is</sup> identical.

Calibration results for US corn markets can be seen in Table IV.A:

|Tabl|e IV.A|||
|---|---|---|---|
|Description|Variable|Value|Source|
|Discount factor|�|0:995|Literature|
|Demand elasticity|!|0:18|IV|
|Supply elasticity|�|0:15|Literature|
|Demand persistence|�z|0:64|AR(1) Zt|
|Supply persistence|�A|0|AR(1) At|
|Steady State productivity|�A|1|Normalization|
|Steady State demand level|�Zy|0:25|Normalization|
|Inventory adjustment cost quarters I,II,III|�<sup>I</sup>|0:0204|Model calibration|
|Inventory adjustment cost quarter IV|�<sup>II</sup>|0:046|Model calibration|
|Yield volatility|�A|0:098|Stand Dev At|
|Demand volatility|�Z|0:018|Stand Dev Zt|
|Public signal A st dev|�<sup>�pu</sup><br>A|0:06|USDA Yield forecast|
|Public signal Z st dev|�<sup>�pu</sup><br>Z|0:048|USDA Demand forecast|

3.2.3 Step 3 30
<!-- Start of picture text --> 0.38 | |<br>0.6 I — observed price I i<br>ly) ——-—-model price series | |) ih<br>4 14 | s<br>0.4 lf!\ 1] | 1k |ee|<br>i | Hert Mae<br>0.2 ry: fl ‘Iri [}o4iy<br>ifit Y ' Ly<br>Vy. \ ”<br>rt<br>of 4 In , | Nf<br>VI IK, i; Uf<br>- 0 .2 1Ii! euLa [ tl ; fpr!2<br>1 : Vfl<br>-0.4 ' 1 | ll \<br>| ly I<br>-0.6 hoyi<br>|<br>-0.8<br>1975 1980 1985 1990 1995 2000 2005 2010 2015 2020<br><!-- End of picture text -->
<!-- Start of picture text --> 0.8<br>0.6<br>0.4 |<br>0.2 |<br>0<br>-0.2<br>-0.4<br>-0.6<br>1975 1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
# 3.2.4 Step 4

A key innovation of the model is the incorporation of both private and public signals into agents’ decisions. Agents use these signals to predict the annual component of demand and yields. They have both private and public sources, and weight them proportional to their precision. The model makes use of USDA reports released monthly that predict future demand and yield per acre; they are considered be public signals since anyone can access them at no cost. The section then estimates private signals through a Kalman Filter, in which the observables are prices and ex post realized annual demand and yield values.

Formally: where �� and �" are covariance matrices for �t; "t: �� is calibrated by measuring the precision of public forecasts and the standard deviation of changes in price that remain unexplained by the model. Values for �";are the precision in private forecasts estimated previously. Matrices Ft; Ht; and Bt represent the laws of motion for private signals, the e¤ect of private signals on prices, and the e¤ect of the rest of state variables on prices, respectively. Also, the second and third rows of matrix Ht represent the relation between signals and ex post realizations. That is, they capture the fact that signals forecast ex post realized demand and supply shocks with some error.

Estimations can be seen in Figures X and XI, which show the estimated private signal. Although private and public signals tend to move together, as one would expect, there are several moments in which these di¤er, which may explain public information is not the only driver of expectations.

33
<!-- Start of picture text --> 0.15<br>0.1<br>-0.1<br>-0.15<br>-0.2<br>0.25 estimated privateA signal<br>EEE public A signal<br>-0.3<br>1980 1985 1990 1995 2000 2005 2010 2015<br><!-- End of picture text -->
<!-- Start of picture text --> 0.25<br>0.15<br>0.1<br>.-0.1 vim vy!<br>-0.15<br>4980. 1985 1900 1908 2000 2005 2010 2016<br><!-- End of picture text -->
<!-- Start of picture text --> 0.8<br>L__Jvield<br>0.6 2 Quarterly Demand Shock<br>MW Stocks<br>04 ME Annual Demand Shock<br>HB Residual<br>0.2 |<br>-0.2 2 ER EOE<br>-0.4<br>-0.6<br>-0.8<br>-1<br>1987.5 1986 1988.5 1989 1989.5 1990 1990.5 1991 1991.5 1992 1992.5<br><!-- End of picture text -->
Table IV.B Fraction of Price Change Due to Each Variable*

|Variable|Description|Fraction|
|---|---|---|
|�<sup>Apr</sup><br>t|Supply Private Signal|0:056|
|�<sup>Zpr</sup><br>t|Demand Private Signal|0:099|
|At|Productivity|0:018|
|"<sup>Z</sup><br>t|Quarter Demand Shock|0:089|
|Xt|Inventories|0:088|
|�<sup>Apu</sup><br>t|Supply Public Signal|0:009|
|�<sup>Zpu</sup><br>t|Demand Public Signal|0:019|
|Zy�1|Past Demand Level|0:043|
|At�1|Past Productivity|0|
|"<sup>Z</sup><br>y|Annual Demand Shock|0:274|
|Residual||0:305|

*in absolute values

# 4 Conclusion

This paper addresses the issue of agricultural commodity price changes throughout the past decades. In particularly, the paper takes the case of corn for US markets. It derives two analyses: long run and short run. In the ...rst, it initially runs a sign restricted VAR as a benchmark, ...nding that demand and speculation are the biggest drivers of annual changes. It then contrasts this with a simple model in which it simulates theoretical prices, such that demand and supply match each year. That is, it estimates the price that would have theoretically cleared the market (no inventory changes), then compares it against the observed prices. The intention was to develop what one could consider a proxy for a non-distorted price and compare to see whether the observed price was too far away from it. Results show that after the 1996 farm bill, the relationship between these two time series is very close. That is, there does not seem to be a major di¤erence between the marketclearing price and the observed price. Before 1996, observed prices clearly di¤ered from theoretical ones. There are several explanations for this, but a major one is that government agriculture policy 37
intervened heavily, mostly through price-sustaining policies. These were instrumented by either government accumulation of stocks (the CCC program) or subsidizing the private sector to do that for them (the FOR program). After 1996, government policy became more market friendly by introducing price ‡oors below equilibrium and limiting the government’s budget available for stocks. Interestingly, annual changes are mostly explained by supply shocks, in contrast ith the VAR approach. When looking at overall changes through time, Figure II.A shows that no big distortions are to blame for price hikes in the 2000s. Moreover, a more detailed analysis shows that the emergence of an energy-related source of demand for corn had a signi...cant impact, and explains an important aspect of price increases in 2005-2010. This is in line with the increasing positive correlation between corn prices and energy ones. An important thing to note is that government mandates could have played a major role in this. Therefore, it could be that we are observing a shift in regulation type from direct purchases to private coercion. Identifying these interventions, quantifying them, and estimating their economic impact are subject’s for future research.

The second part of the paper analyzes the short run. It develops a quarterly based model in which agents can only produce at certain quarters, as in most agricultural markets. It then linearizes it and analyzes second order moments. When focusing on a higher frequency, there is space for speculation to play an important role, since it is possible to make pro...ts by storing for short periods of time and reselling. In other words, it is irrational for inventories to go up forever, but it is perfectly possible that they increase for one or two quarters. Therefore, the paper proceeds by modeling speculation and introduces a theoretical innovation: information shocks. Given that storage is by de...nition related to expectations about future prices, the information available at each moment is key to inventory decision-making. The model has two sources of information: public and private. Public information comes as a forecast by a government agency (in this case, the USDA). Private information comes from information markets (consulting ...rms, private research departments, etc.). These reports help agents form expectations about what future prices might be and make decisions accordingly. Given that USDA reports are publicly available, and that they contain quantitative forecasts for demand and supply, the model is able to estimate their impact on market prices. It also identi...es the precision of private signals and estimate a time series for them. Results show that as one would expect, demand and supply shocks account for a large fraction of price changes— as much as 52%. However, this leaves a relevant space for speculation or inventory 38
shocks. Information shocks (which act by inducing agents to buy or sell their stored goods) can explain an additional 18%. A remaining 31% is due to factors not included in the model but that alter storage decisions, as well as second-order e¤ects in demand or supply. The second section quanti...es by how much these unexplained factors can in‡uence observed prices. Finally, another important result is that non-explained sources of price changes, whatever these may be, do not seem to be any more relevant in the 2000s than they were before. This again con...rms once more that the idea that nonfundamental factors have increased in importance is not sustainable.

Results show that in the short run, prices can deviate severely from fundamentals, even though in the long run that is not the case. Given that the market analyzed here is well developed in terms of liquidity and transparency, this raises questions regarding how informative prices may be in the short run, with important implications with respect to GDP accounting and theoretical modeling. As in Romer (2016), my results challenge the notion of market prices as a result of a standard pro...t- and utility-maximizing framework.

In conclusion, the evidence presented here indicates that there is no evidence for the hypothesis that corn markets arti...cially deviated from fundamentals in the long run, but does allow the possibility for quarterly frequencies. As an innovation, this paper also shows the important role information shocks play in the short run. Unknown sources of variability are quanti...ed, but are yet to be explained. Further research in this respect is necessary.

39