U.S. Farm Policy and the Variability of Commodity Prices and Farm Revenues. Sergio H. Lence. and. Dermot J. Hayes*

Transcription

1 U.S. Farm olicy and the Variability of Commodity rices and Farm Revenues Sergio H. Lence and Dermot J. Hayes* aer resented at the NCR-134 Conference on Alied Commodity rice Analysis, Forecasting, and Market Risk Management Chicago, Illinois, Aril 17-18, 2000 Coyright 2000 by Sergio H. Lence and Dermot J. Hayes. All rights reserved. Readers may make verbatim coies of this document for non-commercial uroses by any means, rovided that this coyright notice aears on all such coies. *Associate rofessor and rofessor resectively, Deartment of Economics, Iowa State University, Ames.

2 1 U.S. Farm olicy and the Variability of Commodity rices and Farm Revenues ractitioner s Abstract A dynamic three-commodity rational-exectations storage model is used to comare the imact of the Federal Agricultural Imrovement and Reform (FAIR) Act of 1996 with a free-market olicy, and with the agricultural olicies that receded the FAIR Act. Results suort the hyothesis that the changes enacted by FAIR did not lead to ermanent significant increases in the volatility of farm rices or revenues. An imortant finding is that the main economic imacts of the re-fair scenario, relative to the free-market regime, were to transfer income to farmers and to substitute government storage for rivate storage in a way that did little to suort rices or to stabilize farm incomes. Keywords: FAIR Act, rice volatility, storage. Introduction Historically, the U.S. government has had a substantial involvement in the agricultural sector. Since 1988, annual U.S. government exenditures in suort rograms for all cros ranged from a low of $6.3 billion in 1996 to an estimated high of $24.2 billion in 2000 (Food and Agricultural olicy Research Institute). From 1988 to 1995, government exenditures averaged $3.4 billion er year on rograms alone. This increased to $4 billion er year between 1996 and 2000, after assing the Federal Agricultural Imrovement and Reform (FAIR) Act in The FAIR Act reresented a major shift in U.S. agricultural olicy. It relaced farm rice suort rograms with direct ayments, removed restrictions on the tyes of cros that farmers could lant or the amount of acres that farmers had to idle to qualify for suort rograms, and introduced an alternative to the loan rate rogram called the "loan deficiency ayment" (LD). 1 The FAIR Act is likely to have a noticeable imact on U.S. agriculture. In articular, on, soybean, and wheat markets, as these are the commodities most directly affected by the secific changes introduced by the FAIR Act. Interestingly, the markets for, soybeans, and wheat have also deicted extraordinary volatility (in both rices and stocks) in recent years. Many have attributed this volatility to the FAIR Act itself. This linking of the Act with recent market behavior makes some sense, as the Act reduced the reliance on government storage and eliated the target rice rogram. However, the FAIR Act also allows roducers to resond in a more flexible way to changes in market conditions, thereby damening the influence of weather shocks. It is also ossible that the rivate sector might undertake the storage activities formerly done by the government, and that it might do 1 The loan rate rogram in lace before the FAIR Act allowed farmers to borrow (at a county-secific loan rate er bushel) against stored grain and to reay this loan only when market rices made it worthwhile to the farmer. This rogram resulted in government-owned storage and may have ut a floor under commodity rices. Under FAIR, the LD rogram was introduced to reduce government involvement in stocks, and offers farmers a choice between the loan rogram and a direct ayment equal to the difference between local cash rices (as measured by the government) and the loan rate.

3 2 so in a way that makes more economic sense. Because these asects of the FAIR Act may induce lower rice volatility, the net effect is unknown. The ultimate imact of the FAIR Act will not be known until the market has reached a new equilibrium, and this will take decades. The roblem addressed here is the behavior of rices, stocks, and other market variables of interest for, soybeans, and one other cro under the FAIR Act regime. It is assumed that rivate market articiants hold rational exectations and behave in an otimal fashion. The analysis is conducted by solving for the equilibrium market conditions that satisfy the otimal behavioral atterns of all those involved. The seculative rational exectations storage model that is used is based on Williams and Wright, Deaton and Laroque (1992, 1996), and Chambers and Bailey. In addition, the resent study is the first one to solve for intertemoral market equilibrium in three markets simultaneously, allowing for storage as well as random shocks in both suly and demand schedules. Modeling three markets simultaneously enables exlicit incororation of otentially imortant outut substitution effects. Endogenous derivation of storage demand ensures the internal consistency of the model, as olicy changes imly changes in the robability density functions of rices, which in turn should change the demand for storage. Imortantly, this analysis avoids the famous Lucas critique, as the model built deends only on behavioral arameters that are not affected by shifts in olicy regimes such as the one under consideration. Model Secification It is assumed throughout that there are three storable commodities:, soybeans, and "others." Attention is restricted to three commodities because (a) the study's rimary objective is to uncover the otential effects of the FAIR Act on the U.S. markets for and soybeans, and (b) exlicitly modeling many commodities is comutationally intractable due to the "curse of dimensionality" (e.g., Judd,. 430). 2 Historically, U.S. agricultural olicies directly affected the suly of and soybeans (Lee and Helmberger), as well as their storage demand. For this reason, the model secifications under the benchmark setting of no government intervention, and the two intervention scenarios of re-fair and FAIR regimes are discussed in more deth in the next three subsections. Benchmark Setting: No Government Intervention Cro roduction takes one eriod from lanting to harvest. Outut of cro j (j = 1,, J) at time t + 1 (O jt+1 ) is a function of the acres of all J cros lanted at time t (A 1t,, A Jt ) times the realization of an outut shock at time t + 1 (e Ojt+1 ): (1) O jt+1 O j (A 1t,, A Jt ) e Ojt+1. 2 For examle, the commodity roblem analyzed here requires us to solve for J 72 J unknowns in J 72 J nonlinear equations for each scenario, where J is the number of commodities analyzed. That is, going from 3 to 4 commodities imlies a 96-fold increase in the number of unknown variables that have to be solved for, from 1,119,744 to 107,495,424.

4 3 Actual roduction at time t + 1 is random from the ersective of time t because yields are stochastic due to weather, ests, etc. Similarly, actual rices at time t + 1 ( jt+1 ) are random from the standoint of time t, due to stochastic outut as well as stochastic demand. Because of outut uncertainty, roducers are assumed to make their lanting/inut decisions at time t so as to maximize exected rofits at t + 1 (π t+1 ), conditional on their information at time t (E t ( )) and subject to any existing constraints. That is, at time t roducers choose A 1t through A Jt to maximize: (2) E t (π t+1 ) = E t ( J j= 1 O jt+1 jt+1 ) C(A 1t,..., A Jt ), J = j= 1 O j (A 1t,, A Jt ) E t (e Ojt+1 jt+1 ) C(A 1t,..., A Jt ), (2') J = j= 1 O j (A 1t,, A Jt ) jt 1 + C(A 1t,..., A Jt ), where C( ) is the cost function, and jt + 1 E t (e Ojt+1 jt+1 ) is equal to (a constant times) the roducers' incentive rice or action certainty equivalent rice for commodity j (Wright; Newbery and Stiglitz). In general, jt + 1 E t (e Ojt+1 ) E t ( jt+1 ) because roducers recognize that their yield disturbance is roortional to the aggregate outut, and the latter covaries with the market rice. Objective function (2 ) is quite general in that it allows for very comlex interactions among individual cro oututs and costs (e.g., Lin and Riley). Under standard regularity conditions for the outut and cost functions, the acreage suly schedules are obtained from the first order conditions (FOCs) corresonding to (2 ). Assug erfectly cometitive outut markets and no binding constraints at the otimum, the FOCs can be rearranged in a straightforward manner so as to obtain the following first-order logarithmic aroximation to the acreage suly schedules (Chambers,. 167): 3 (3) ln(a jt ) = α Oj + J k= 1 kt 1 β Ojk ln( + ), j = 1,, J. Acreage suly schedule (3) is suitable for numerical simulations because it constrains lanted areas to be strictly ositive, allows for cross effects, and requires only the secification of ownand cross-rice suly elasticities. For these reasons, and also because of numerical tractability, (3) is used in the resent study when there are no binding constraints on the acreage lanted. 3 This logarithmic aroximation imlies exansion around a vector of ones, which is consistent with the normalization used for the resent simulations (see the Model Initialization section below).

5 4 To ensure consistency with stylized facts, the following arameter restrictions are imosed on (3): (a) β Ojj > 0, (b) β Ojk j < 0, and (c) j β Ojk > 0. Condition (a) is necessary and sufficient for the area lanted with cro j to resond ositively to its own roducers incentive rice. Restriction (b) is necessary and sufficient to have cro substitution (through acreage shifts) in resonse to relative changes in roducers incentive rices. Finally, condition (c) ensures that the total area lanted increases if all roducers incentive rices increase by the same ercentage amount. Restriction (c) is also sufficient for the acreage lanted with a articular cro to exand if the roducers incentive rices for all cros go u by the same ercentage amount. Realistic modeling also requires that (a) acres lanted with individual cros be strictly ositive, and that (b) the total area lanted with cros not exceed the total number of acres of arable land ( A). 4 As mentioned earlier, acreage suly schedule (3) automatically meets restriction (a). As for (b), it is assumed that when the total acreage constraint is binding, the acreage suly schedules are roortional to the unconstrained acreage suly schedules. That is, acreage suly schedules are given by (4) instead of (3) when the latter violate the restriction A A: j jt (4) ln(a jt ) = α Oj + J j= 1 kt 1 β Ojk ln( + ) + ln( A) ln[ J j= 1 ex(α Oj ) ( J k= 1 β kt+ 1) Ojk ], j = 1,, J. To derive (4), denote acres calculated from (3) by Å jt, to distinguish them from acres obtained by means of (4). After omitting nonessential subscrits and suerscrits to avoid cluttering, (3) may be re-written as Å j = ex(α j ) k β. Hence, total acres from (3) are Å Σ j Å j jk = Σ j ex(α j ) k k (> A if total acreage is binding). But A j = Å j A/Å if constrained acreage suly schedules (A j ) are to be roortional to unconstrained acreage suly schedules (Å j ) (note that Σ j A j = A by construction). Exression (4) is finally obtained by taking natural logarithms on both sides of A j = Å j A/Å. β Commodity j s aggregate demand for current consumtion is ostulated to be as follows: k jk (5) D jt = α Dj + β Dj 1 γ Dj 1- jt Dj γ + e Djt, where D jt denotes quantity demanded for current consumtion at time t; α Dj, β Dj, and γ Dj are demand function arameters; and e Djt is a zero-mean demand shock in eriod t. arameter γ Dj reresents the relative curvature arameter of the (direct) demand curve (Wright). Demand curvature increases with γ Dj, demand being linear (strictly convex) when γ Dj = 0 (γ Dj > 0). Demand function (5) includes both domestic and international comonents. One could easily include a searate exort demand schedule. However, this would add little to the analysis as long as the exort demand is correctly incororated into the total demand function D jt. 4 Restriction (b) is also required to model meaningfully the re-fair regime s set-aside olicy (see next subsection).

6 5 All commodities considered are assumed to be storable, with er-unit storage costs equal to φ j for commodity j. Under cometition, exected-rofit-maximizing seculators will store commodity j u to the oint where it is no longer rofitable to do so. Hence, cometitive equilibrium in all markets entails simultaneously satisfying conditions (6) through (8): (6) I jt+1 = O jt + I jt D jt = Q jt D jt 0, (7) δ E t ( jt+1 ) jt φ j 0, (8) [δ E t ( jt+1 ) jt φ j ] I jt+1 = 0, for j = 1, 2, 3, where Q jt O jt + I jt and I jt are commodity j s total suly and inventory on hand, resectively, at the beginning of eriod t, and δ is the discount factor er eriod. Outut (O jt+1 ) follows from (1), (3), and (4), whereas demand for current consumtion (D jt ) is given by (5). Inequality (6) says that, in equilibrium, total suly of commodity j must be equal to the total demand for it, where total demand is given by demand for current consumtion lus demand for storage. In addition, (6) states that carry-over inventories cannot be negative. According to (7), in equilibrium there cannot be any rofitable oortunities from storing an additional unit of commodity. Finally, condition (8) imlies that (a) no storage will occur (I jt+1 = 0) if storing leads to exected losses (δ E t ( j+1 ) < jt + φ j ), and (b) there cannot be rofitable oortunities available from storage (δ E t ( j+1 ) = jt + φ j ) if storage is strictly ositive (I jt+1 > 0). Government Intervention Scenario 1: re-fair Regime Government intervention in U.S. cro markets evolved gradually through time before the assing of the FAIR Act (e.g., see Hoffman or Gisser for a summary of the history of U.S. government feed grain rograms u to 1989). For this reason, in the resent study the re-fair regime consists of a stylized scenario resembling the major government interventions regarding and soybeans in force immediately before the FAIR Act. Under the re-fair regime, roducers articiating in the government rogram have the right to sell their and soybeans to the government at a reset loan rate (R and R bean ). This rovision of the government rogram effectively creates a floor rice at the loan rate, as articiating farmers get max(r, t ) and max(r bean, beant ) for their time-t outut of and soybeans, resectively. In addition to having access to the loan rate for and soybeans, articiating roducers get a deficiency ayment (d t ), rovided they set aside a certain fraction (0 S t 1) of their base acreage ( B ). That is, the number of set aside acres in year t equals S t B. The base acreage is a reset figure central to the government intervention rogram, and reflects the historical number of acres lanted with. The deficiency ayment is then calculated as (9) d t [A t, (0.85 S t ) B] Y max(0, T t ),

7 6 where T is the target rice and Y is the historical yield for. In (9), the ( ) term means that the number of acres qualified for deficiency ayments can exceed neither the acreage actually lanted with (A t ) nor the eligible acreage ((0.85 S t ) B ). The roduct ( ) Y is an artificial outut figure used for government suort uroses. Finally, the max( ) term means that roducers are aid the difference (if ositive) between the target rice ( T ) and the market rice ( t ) er unit of suorted outut. 5 In summary, the deficiency ayment olicy (9) ensures that roducers get a net rice of at least T for an amount of equal to ( ) Y. The set aside fraction (S t ) in (9) is a key olicy instrument, and is announced by the government every year before lanting time. The 1990 Farm Act stiulates that 0 S t if the revious year s stock-to-use ratio for (I t /D t-1 ) is less than or equal to 25%, and 0.10 S t 0.25 if the revious year s stock-to-use ratio is greater than 25%. Hence, the government is assumed to follow olicy rule (10) to calculate the set aside fraction: (10) S t = S(I t /D t-1 ), where S( ) is a strictly monotonic function, such that S( ) 0 as I t /D t-1 0, S( ) 0.25 as I t /D t-1, and 0.10 S(0.25) Historically, the number of acres actually lanted with (A t ) lus the area considered to be lanted with for government uroses (i.e., the set aside lus 15% of the base acreage) has almost always exceeded the base acreage ( B). 6 Hence, under the re-fair regime the constraint (11) is imosed to model this stylized fact: (11) A t + (S t ) B B. Given constraint (11), the first term in the right-hand side of (9) simlifies to ( ) = (0.85 S t ) B, which imlies that deficiency ayments are indeendent of choice variables (i.e., A jt s). In turn, this means that if the acreage constraint (11) is not binding, the FOCs for the re-fair regime are analogous to the FOCs under no government intervention. Hence, the re-fair acreage suly schedules when the acreage constraint (11) is not binding are given by (3) if total acreage is not binding, and by (4) if total acreage is binding. Of course, under re-fair E t [e Ojt+1 max(r j, jt+1 )] for j = and soybeans, and the total acreage constraint is total acres us set aside acres (Σ j A jt A S t B). If the acreage constraint (11) is binding but total acreage is not, the area is simly A t = (0.85 S t ) B and the acreage suly schedules for soybeans and others are: jt Technically, the max( ) term in (9) should have max(r, t ) instead of t. However, in market equilibrium t R because roducers will never sell their at rices below the loan rate R. 6 It is often argued that the main exlanation for this fact is the roducers fears of losing their base acreage.

8 7 (12) ln(a jt ) = γ Oj + γ Oj ln(a t ) + k γ Ojk ln( + ), j, k = beans, others. kt 1 In (12), γ Oj α Oj γ Oj α O, γ Oj (κ k κ jk κ j κ kk )/(κ jj κ kk κ jk κ kj ), γ Ojj κ kk /(κ jj κ kk κ jk κ kj ), γ Ojk κ jk /(κ jj κ kk κ jk κ kj ), and κ ij is the ijth element of the inverse of the suly 1 elasticities matrix κ O β = [β O11 β O1J ; β OJ1 β OJJ ] 1. Suly schedule (12) is consistent O with (3). To see why, note that (3) is a rearrangement of the logarithmic first-order aroximation to the FOCs: ln( jt + 1 ) = k κ jk [ln(a kt ) α Ok ], j =, beans, others. When the acreage constraint is binding, the FOCs for beans and others become ln( jt + 1 ) = k κ jk [ln(a kt ) α Ok ], j = beans, others, and A t = (0.85 S t ) B. Suly schedule (12) may then be obtained by solving the latter two FOCs for the two unknowns ln(a beant ) and ln(a othert ). Finally, if both the acreage constraint (11) and the total acreage constraint are binding, the area is also A t = (0.85 S t ) B, but the acreage suly schedules for soybeans and others become: (13) ln(a jt ) = γ Oj + γ Oj ln(a t ) + k γ Ojk ln( + ) kt 1 + ln( A S t B) ln[a t + ex(γ Oj ) j Oj A γ t ( k γ kt+ 1) Ojk ], for j, k = beans, others. Exression (13) may be derived from (12) in a manner analogous to the derivation of (4) from (3). To detere the market equilibrium under the re-fair regime, it must be recalled that the government buys all of the and soybeans being offered by farmers at the loan rate level. It is assumed that the and soybeans bought by the government are stored and sold whenever market rices rise above the corresonding loan rates. Hence, for j = and soybeans the equilibrium conditions analogous to (6) through (8) are: (14) jt 1 I + + g jt 1 I + = O jt + I jt + g I jt D jt = Q jt D jt 0, (15) δ E t ( jt+1 ) jt φ j 0, jt R j, (16) [δ E t ( jt+1 ) jt φ j ] jt 1 I + = 0, jt R j, (17) g jt 1 I + = max[0, Q jt jt 1 I + D jt (R j )], g where I jt and I jt denote storage by the rivate and government sectors, resectively, and D jt (R j ) is consumtion when rice equals the loan rate. Total storage is simly the sum of rivate and

9 8 government storage (I jt+1 = I jt + g I jt ). Government intervention in and soybean markets revents their rices from ever falling below the resective loan rates; this condition is reresented by the constraint jt R j. Government Intervention Scenario 2: FAIR Regime Under the FAIR Act, there are neither deficiency ayments nor set aside rovisions. Instead, the FAIR Act lets farmers receive fixed transition ayments as long as they farm the land that had been eligible for ayments under the revious olicy regime (i.e., the former base acreage). These transition ayments are indeendent of the level of market rices and of the cro being grown. The FAIR Act maintains the loan rate rogram. In addition, it introduces a set of LDs by which farmers get the difference between the loan rate and the local market rice on their outut of and soybeans. roducers get the same exected rofits whether they articiate in the loan rate or in the LD rogram, because in either instance the net rices received er unit roduced of and soybeans are max(r, t ) and max(r bean, beant ), resectively. Given that farmers are indifferent between the two rograms, the amount they will sell to the government (under the loan rate rogram) cannot be defined uniquely. Unfortunately, market equilibrium is not well defined in the resence of such indeteracy. To see this, consider the olar cases of farmers that articiate (a) only in the loan rate rogram, and (b) only in the LD rogram. In case (a), market rices will never be below the loan rate. In contrast, in case (b) one may observe market rices well below the loan rate. In ractice, the government has the discretion to slightly modify the secific rules to imlement the loan rate and the LD rograms, so as to make one of them referable over the other. 7 Hence, the market equilibrium indeteracy may be resolved by assug that the government has a olicy rule to favor one rogram over the other. In the resent study, it is assumed that such a olicy rule consists of a imum or floor rice j such that R j j 0, for j = and soybeans. This rule is assumed because, as discussed in the revious aragrah, full loan rate rogram articiation entails a imum rice at the loan rate and full LD rogram articiation yields no imum rice (i.e., a imum rice of zero). Hence, the whole sectrum of ossible market equilibrium outcomes may be sanned by letting j range from 0 through R j. Under the secified assumtions, the FAIR acreage suly schedules are given by (4) if total acreage is not binding, and by (5) if total acreage is binding (with jt + 1 E t [e Ojt+1 max(r j, jt+1 )] for j = and soybeans). Furthermore, for j = and soybeans the equilibrium 7 The LD ayment is suosed to equal the difference between local cash rices and the local loan rate. In reality, the rogram has been run so that the federal government has had a high level of control over the way the local cash rices were measured. It has done this by calculating local cash rices as the difference between rices at exort destinations less some county-secific transortation costs. The government has adjusted these transortation costs to obtain local cash rices yielding the desired LD ayments. For examle, in 1998 there were many instances in which actual local cash rices were between $0.15/bushel and $0.20/bushel above the government estimates of local cash rices. This resulted in artificially large LD ayments and caused most roducers to take the LD ayment rather than to articiate in the loan rogram.

10 9 conditions under the FAIR Act scenario are analogous to (14) through (17), excet that the constraint jt substitutes for the constraint jt R j in conditions (15) and (16). j Numerical Methods To analyze the behavior of storage, rices, roduction, etc., one must first solve for the market equilibrium conditions under each ossible state of the world. This is a difficult task, because the model has no closed-form solution and is highly nonlinear; the model can only be solved and its roerties exlored using numerical techniques. As discussed by Judd (ch. 12 and 17), the storage model may be solved in more than a single way. Here, we adot the method advocated by Williams and Wright, which consists of solving the model by obtaining an aroximation (ψ j ) to the rice exectations conditional on carry-over storage: (18) ψ j (I 1t+1, I 2t+1, I 3t+1 ) = E t { jt+1 [I 1t+1, I 2t+1, I 3t+1 ; ψ j (I 1t+1, I 2t+1, I 3t+1 )]}. Succinctly, the right-hand side of (18) is derived by using direct demand function (5) to exress commodity j s rice as a function of its consumtion demand, jt+1 = g(d jt+1 ), and solving (6) for consumtion to get jt+1 = g(o jt+1 + I jt+1 I jt+2 ). But j s outut (O jt+1 ) is ultimately a function of the current action certainty equivalent rices of all three commodities (from (1) and (3)), which in turn may be exressed as functions of this eriod s carry-overs (I jt+1, j = 1, 2, 3). Further, next-eriod s carry-over of commodity j (I jt+2 ) is also a function of this eriod s carry-overs. Hence, nexteriod s rice of commodity j may be exressed as a function jt+1 ( ) of current carry-overs (I jt+1 ) and the exectation oerator (ψ j ). As ointed out by Williams and Wright, a fundamental advantage of this rocedure is that E t ( ) is a smooth function of I 1t+1, I 2t+1, and I 3t+1. Hence, highly accurate aroximations to E t ( ) may be achieved by means of a relatively low order olynomial function ψ j ( ). This is very imortant for our resent uroses, because the comutational burden of using other methods to achieve the same degree of accuracy with a three-commodity system would be rohibitively high. In the interest of brevity, the full descrition of the comuter algorithm is omitted, but its essence is sketched in Chater 3 of Williams and Wright. Also for comutational efficiency reasons, the function aroximation ψ j ( ) consists of a Chebychev olynomial interolated at Chebychev nodes. In addition, the error robability functions are aroximated by means of Gaussian quadrature techniques, which allow exact calculation of the desired number of moments of the random variables with maximum efficiency. Details about Chebychev interolation and Gaussian quadrature are rovided in Judd. The Chebychev interolation and Gaussian quadrature schemes are calculated by means of the comuter routines develoed by Miranda and Fackler. The rogramg language MATLAB version 5.2 is used to solve the model. Eight interolation nodes er commodity storage ( n I j = 8 j) are emloyed, along with three Gaussian quadrature nodes for each of the six error terms ( n = n = 3 j). The number e Oj e Dj

11 10 of nodes is chosen to obtain an accetable level of accuracy, while maintaining comutational feasibility. For any given storage level, the maximum absolute error in the exected rice aroximation of any commodity is estimated to be less than 0.5%. To give an idea of the large magnitude of the roblem at hand, the key ste in the solution requires solving 1,119,744 (= J j n I j n eoj n edj ) nonlinear equations in as many unknowns. For the simlest scenario ( No Government Intervention ), a single additional iteration at the otimum lasts 25 utes with a entium 450 MHz chi and 260 megabytes of RAM. Model Initialization Numerical solution to the storage roblem is greatly enhanced by normalizing the system so as to avoid variables of significantly different orders of magnitude. For this reason, and also to facilitate the interretation of the model results and arameters, the behavioral arameters are chosen so that equilibrium acreage, outut, and consumtion of each commodity is 1.00 when neither suly nor consumtion demand are stochastic (and, therefore, there is no storage). Sace constraints revent us from reorting simulation results from all of the arameter combinations analyzed. Results for only a single set of arameter values are shown for the No-Government- Intervention and re-fair regimes. For the FAIR regime, results from four alternative arameterizations are rovided. These arameter values were selected so as to be consistent with the corresonding existing literature, and are discussed next. Results for other arameterizations are available from the authors uon request. Suly: The own- and cross-rice elasticities of suly are assumed to be 0.4 and 0.15, resectively. This imlies that α Oj = 0, β Ojj = 0.4, and β Ojk = 0.15 for j and k j. The amount of arable land is hyothesized to be 2% greater than the total acreage devoted to cros in the nonstochastic equilibrium scenario, so that A = Finally, outut shocks (e Ojt+1 ) are assumed to be trivariate normally distributed with a mean of one, standard deviations of 0.16 for, for soybeans, and for others, and correlations of 0.8 for -soybeans, and 0.3 for -others and soybeans-others. Demand: The elasticity of demand for current consumtion is set at 0.6, which with isoelastic demand (α Dj = 0) imlies that γ Dj = 1.6 and β Dj = Demand shocks are assumed to be indeendently and identically distributed with a mean of zero and standard deviations of 0.08 for, 0.07 for soybeans, and 0.06 for others. Storage: Annual er-unit storage costs are hyothesized to be 2% of the non-stochastic equilibrium rice (i.e., φ j = 0.02), and the discount factor is set at δ = 0.95 (which imlies an annual interest rate of 1/δ 1 = 5.26%). 8 Results show that the level of rice volatility (though not the cross-olicy comarison) is very sensitive to the magnitude of the demand elasticity. Therefore, the reorted results corresond to a demand elasticity that gave a rice volatility similar to that exerienced during the re-fair eriod. The sensitivity of the rice volatility to the magnitude of the demand elasticity may suggest a more accurate way of estimating rice elasticities when volatility levels are known.

12 11 Government Intervention under re-fair Regime: Loan rates for and soybeans are assumed to be below the nonstochastic equilibrium rice and relatively favorable to (i.e., R = 0.90, R bean = 0.85). It is also assumed that the target rice is 45% higher than the loan rate (i.e., T = 1.45 R = 1.305), the base acreage is the same as the nonstochastic equilibrium acreage (i.e., B = 1.00), and the historical yield is identical to the mean yield ( Y = 1.00). Finally, the set aside function (10) used is: (19) S t = (I t /D t-1 )/[ (I t /D t-1 )]. It can be easily verified that the right-hand side of (19) satisfies the required conditions for S( ). Government Intervention under FAIR Regime: The loan rate is assumed to be the same as under the re-fair regime (i.e., R = 0.90). For soybeans, results are reorted for both R bean = 0.85 (i.e., the same as in re-fair) and R bean = The motivation for this articular sensitivity analysis is that, even with constant noal loan rates, the level of suort for soybeans relative to may have increased due to lower roduction costs associated with the recent introduction of soybean varieties tolerant to the herbicide glyhosate. Results The simulation results are resented in Tables 1 through 4. The results in Tables 1 and 2 are based on a loan rogram that slightly favors (R = 0.90, R bean = 0.85). Table 1 shows the secific results for, and Table 2 shows the results for soybeans. The first column in Tables 1 and 2 shows the base values of the key economic arameters in the absence of government intervention and without uncertainty. These values are reorted for comarison uroses, and are normalized to equal 1, 0, or 100. The second column shows how these key variables change when uncertainty is introduced. This scenario has no government intervention and is also used as a basis for comarison. The third column shows the results for the re-fair regime, and the last two columns show results for two extreme versions of the FAIR rogram. The first of these (FAIR) shows results when the government sets the LD ayments so that farmers always find the loan rogram to be attractive, thereby allowing the loan rogram to create a imum rice or rice floor. This would be done by adjusting the LD ayment so that farmers referred the loan rogram to the cash LD, i.e., by setting the ayment below the fair remium for the call otion imlicit in the loan rogram. The second scenario (FAIR-ay) assumes that the LD is always the more attractive otion. In this scenario the loan rogram does not suort rices. For each variable of interest, the mean (in bold characters), the 5% quantile, the median, and the 95% quantile are reorted. Whenever useful, the coefficient of variation is also rovided. Table 3 reeats the results shown in scenarios FAIR- and FAIR-ay using a slightly higher relative loan rate for soybeans (R bean = 0.95). The motivation for this sensitivity analysis is that the relative costs of roduction for and soybeans may be changing, as soybean varieties resistant to the herbicide glyhosate come on the market. If this relative roduction cost adjustment is underway, then the effectiveness of the soybean loan rate will increase relative to even if the two noal rates are constant.

13 12 The fourth table shows the two relative loan scenarios (R bean = 0.85 and R bean = 0.95) under an intermediate FAIR rogram regime where some grain enters the loan rogram and the government ays the LD on the remainder. In this regime, the loan rogram acts to imose imum rices, but the imum rice levels are below the loan rates. In order to calculate these results, the model was calibrated so that the resulting imum rices were half way between the loan rates and the 5% lower rice quantiles of the FAIR-ay scenario. For examle, as shown in Tables 1 and 2, when the loan rates for and soybeans are R = 0.90 and R bean = 0.85, the resective 5% lower rice quantiles under FAIR-ay are 0.82 and Therefore, the intermediate scenario for R = 0.90 and R bean = 0.85 is calibrated so that the imum rices for and soybeans equal = 0.86 and = 0.85, resectively. bean Discussion The most interesting comarison in Tables 1 and 2 is that between the regime with random effects and no government intervention (i.e., the free-market scenario) and the re-fair regime. These results show that the re-fair rogram resulted in a very modest reduction in roduction and a negligible effect on market rices. This was true desite rograms that took land out of roduction and that created large government-controlled stocks. The results indicate that the acreage reduction rograms were not effective because they removed land that might not have been farmed under the free market scenario. The intuition is that land allocation decisions resonded to rices, and when rograms ulled some land out of roduction other (ossibly less roductive) land came into roduction. This similarity would have been comounded by a government rogram that took land out of roduction when stocks were high (as was the case for under re-fair), because the free market would also have ulled land out of roduction in these surlus eriods. In addition, the amount of rivate storage of under the free-market scenario is double that under the re-fair regime, again suggesting that some of the government intervention was crowding out an activity that the rivate sector would have undertaken in a normally-functioning free market. The greatest imact of the re-fair rogram is that farm revenues from are substantially higher than under the free-market regime. This additional income is a result of the target rice rogram, which rovides farmers with free "in-the-money" ut otions. Because of the way the target rice rogram was modeled, high target rices did not have an imact on acreage at the margin. This is true because deficiency ayments were based on 85% of historic roduction and not on the actual acreage lanted with, as long as the latter exceeded the eligible acreage (recall discussion of exression (9)). The coefficient of variation of farm incomes in the re-fair scenario (12% for and 11% for soybeans) is lower that in the free-market scenario (14% for and 11% for soybeans). However, this reduction seems too small to justify the re- FAIR regime as a means to rovide income stability. Further evidence in this regard is that the difference between the median and the lower 5% quantile of farm revenues from was actually smaller under the free-market regime (0.20 = ) than under re-fair (0.24 = ). One reason for the re-fair rogram failure to stabilize income is that deficiency ayments tend to be negatively correlated with market rices (see (9)), but are correlated with roduction only indirectly, to the extent that the latter is correlated with rices. Therefore, deficiency ayments sometimes come at a time when revenues are high, and sometimes fail to come when cro yields were low. This effect is almost enough to offset the other revenue stabilizing effects of the re-fair rogram.

14 13 In summary, the key economic imacts of the re-fair scenario were to transfer income to farmers and to substitute government storage for rivate storage, in a way that did little to distort rices or to stabilize farm incomes. The remaining results in Tables 1 and 2 show the effect of the two extreme versions of the FAIR rogram. In the first of these (FAIR-), the rogram is oerated to rovide a imum rice equal to the loan rate, by making it otimal for farmers to ut grain in the loan rogram. In the second (FAIR-ay), the rogram is run so that all farmers find it otimal to take the LD ayment instead of the loan. This is modeled as a choice between the call-otion remium that is imlicitly included in the loan rogram and the direct ayment that is the LD. Whenever the government offers a direct ayment that is greater than the fair otion remium, farmers are assumed to resonse otimally by taking the direct ayment. The rincial imact of the assumtion about the way the FAIR rogram is run shows u in the amount of storage. As might be exected, whenever the government runs the FAIR rogram to ro u rices, the government ends u storing a lot of grain. Another difference between the FAIR- and the FAIR-ay regimes is that the latter exhibits higher rice volatility for, as evinced by a coefficient of variation of 23% versus 20% for FAIR-. This is to be exected, as rices under FAIR- are not allowed to dro below the imum level, and are usually revented from taking high values because of the significantly higher (mostly government) stock levels. The imact of the FAIR rogram assumtions on other economic arameters is relatively muted in large art, because market forces adjust to offset the imact of the rogram changes. Table 3 shows the two extreme FAIR regimes with a higher suort level for soybeans. The imact of this change is to dramatically increase government storage of soybeans in the FAIR scenario and to increase loan deficiency ayments for soybeans in the FAIR-ay scenario. It is interesting to note the degree to which government storage crowds out rivate storage when government storage of soybeans increases. For FAIR-, increasing the loan rate for soybeans from R bean = 0.85 to R bean = 0.95 induces a fall in the average rivate storage from 0.05 to 0.01, and an increase in government storage from 0.01 to Averages can be very misleading in both cases, because the storage distributions have very long tails. 9 As may be inferred from the storage quantiles, average government storage is so high because there are a few years when stocks kee accumulating, which is something that is ossible without any mechanism to restrict roduction. These few years will greatly inflate the average. The results just discussed show how imortant it is to have a feedback mechanism built into government rograms involving imum rices. Note that mechanisms were in lace under re-fair to restrict roduction that are absent under FAIR. Under FAIR, farmers find it rofitable to roduce soybeans at the imum rice of 0.95 (as median soybean roduction is 1.00 and median soybean rice is 0.95), so farmers get neither a signal to reduce roduction nor are ever 9 Average storage is calculated by adding u the amounts stored each year and dividing this sum by the number of years.

15 14 forced to reduce roduction. 10 The FAIR- rogram, results of which are shown in Table 3, does not have this built-in feedback mechanism; hence, there is a otential for large accumulations of government stocks. The reason the average rivate storage is 0.01 and not 0.00 in this scenario is that there may be a string of oor harvests, in which case government will store nothing but rivate storage will be rofitable. rivate storage never coexists with government storage; i.e., there can only be rivate storage in those years in which there is no government storage. Comarison of Tables 1 and 3 reveals that increasing the soybean suort from R bean = 0.85 to R bean = 0.95 has a very small imact on. There is a very small increase in the average rice of in the FAIR-ay scenario (from 1.02 to 1.03), and an offsetting reduction in the government exenditures on LD. Table 4 shows a more realistic intermediate FAIR scenario. The first and third columns of results can be comared with the re-fair and free-market scenarios in Tables 1 and 2. Considering first, the intermediate FAIR regime results in more government storage and total average storage, slightly lower rices, and an offsetting deficiency ayment not in the free-market scenario. rice volatility is slightly lower under the FAIR scenario because of the increased storage. Comaring FAIR with the re-fair scenario, the most noticeable effect is a one-to-one substitution of government storage and rivate storage (0.06 and 0.08 versus 0.08 and 0.06). The level of rice volatility is almost unchanged, with coefficients of variation of 21% for re-fair and 22% for FAIR. Farm revenues under re-fair are remarkably higher because of the transfer effect of the re-fair deficiency ayments. However, farm revenue volatility (as measured by the coefficient of variation) is relatively constant across the two government-intervention scenarios. 11 Unsurrisingly, soybean results for the intermediate scenario with a loan rate of R bean = 0.85 are almost the same as for the free-market and re-fair regimes. This is true because such a soybean loan rate level under re-fair had little imact on the soybean market relative to the freemarket scenario (see Table 2). An increase in the soybean loan rate from R bean = 0.85 to R bean = 0.95 causes average total storage of soybeans to increase from 0.06 to Such growth in storage is a consequence of the great exansion in government stocks (from 0.01 to 0.05), as rivate stocks actually decrease from 0.05 to Government storage exands due to the urchases required to suort the imum rice, which is increased (from 0.85 to 0.89) along with the loan rate increase. The soybean loan rate increase also causes average soybean rice and its volatility to fall slightly (from 1.02 to 1.01 and from 17% to 16%, resectively). The reduction in average rice is a direct consequence of the higher level of stocks, which translates into larger total suly. 10 It could be argued that the actual FAIR regime has such a built-in mechanism. If stocks do start to accumulate, the government can change the arameters of the LD rogram to make the LD ayment referable to the loan rogram. To do this it would reort a osted cash rice (C) that is lower than actual cash rices in that county on that date. Because the LD ayment equals the loan rate us the C, the use of a smaller C will increase the incentive to take the cash ayment instead of utting the grain under loan. However, this feedback mechanism is not described in any official ublications, so it is difficult to incororate this ossible feedback mechanism in the resent analysis. 11 The analysis excludes the direct transition ayments included in the actual FAIR rogram. These ayments are equal to about 10% of the value of outut. If transition ayments were included in the FAIR farm revenues, the re- FAIR rogram would continue to have substantially higher farm revenues.

16 15 Further, because of the reduction in average soybean rice and the higher soybean loan rate, deficiency ayments shoot u from 0 to Finally, average farm revenues from soybeans increase by the same amount as the increase in government deficiency ayments. The reason for this is that, as it is aarent from Table 4, most of the government exenditures occur as deficiency ayments as oosed to storage oerations. Figures 1, 2, and 3 show the rice distributions that are generated under the freemarket, re-fair, and intermediate FAIR scenarios, resectively. 12 Each figure shows the rice distribution under low, median, and high beginning storage levels for. It is immediately clear that all of the distributions are skewed to the right. Deaton and Laroque exlain why these skewed rice distributions occur in commodity markets. Large uside rice movements will occur when sulies are tight because storage cannot be negative. Symmetrically low rices do not occur because seculative storage will take lace when rices dro below the level at which one can rationally exect to rofit from storage. Under the free-market scenario, both the skewness and the mean rice level increase as storage falls. When yields are high, the absence of any rice suort olicy allows market rices to fall as low as about 75% of the (unconditional) exected level, even if beginning stocks are low. The distributions for the FAIR and re-fair scenarios are truncated at the rice level where government storage occurs. The re-fair results show that in years when carry-in stocks are high, there is about a 61% robability that the loan rogram will suort rices. The comarable value for the intermediate FAIR scenario is about 53%. However, this value deends on the arbitrary assumtion about the way the LD rogram is imlemented. Concluding Remarks A dynamic rational-exectations model of commodity markets allowing for storage and outut substitution among three commodities is advanced to analyze the imact of the Federal Agricultural Imrovement and Reform (FAIR) Act of The advantage of this model being used for the intended uroses is that the well-known Lucas critique does not aly, as the model built deends only on behavioral arameters that are not affected by changes in olicy regimes such as the one being studied. It is found that the transitional ayments created to relace the re-fair deficiency ayments are much lower than the ayments they relace and this does reduce farm revenues. However, these revenue losses are not a result of low market rices. The results also lend suort to the hyothesis that the changes made when FAIR was enacted did not lead to a ermanent significant increase in the volatility of farm rices or revenues. An imortant finding is that the main economic imacts of the re-fair scenario, relative to the free-market regime, were to transfer income to farmers and to substitute government storage for rivate storage in a way that did little to distort rices or to stabilize farm incomes. 12 Figure 3 deicts the intermediate FAIR regime with the high soybean loan rate (R bean = 0.95). The grah for the low soybean loan rate (R bean = 0.895) is omitted in the interest of sace, as it is similar to Figure 3.

17 16 References Chambers, Marcus J., and Roy E. Bailey. A Theory of Commodity rice Fluctuations. Journal of olitical Economy 104(1996): Chambers, Robert G. Alied roduction Analysis A Dual Aroach. Cambridge, MA: Cambridge University ress, Deaton, Angus, and Guy Laroque. Cometitive Storage and Commodity rice Dynamics. Journal of olitical Economy 104(1996): On the Behavior of Commodity rices. Review of Economic Studies 59(1992):1-23. Food and Agricultural olicy Research Institute. FARI 2000 U.S. Agricultural Outlook. Staff Reort #1-00, Iowa State University, Ames, and University of Missouri, Columbia, Gisser, Micha. "rice Suort, Acreage Controls, and Efficient Redistribution." Journal of olitical Economy 101(1993): Hoffman, Linwood, ed. "U.S. Feed Grains: Background for 1990 Farm Legislation." Washington, DC: Economic Research Service, U.S. Deartment of Agriculture, Agriculture Information Bulletin Number 604(May 1990). Judd, Kenneth L. Numerical Methods in Economics. Cambridge, MA: The MIT ress, Lee, David R., and eter G. Helmberger. "Estimating Suly Resonse in the resence of Farm rograms." American Journal of Agricultural Economics 67(1985): Lin, William, and eter A. Riley. "Rethinking the Soybeans-to-Corn rice Ratio: Is Still A Good Indicator For lanting Decisions?" Washington, DC: Economic Research Service, U.S. Deartment of Agriculture, Feed Situation and Outlook Yearbook FDS-1998 (Aril 1998): Lucas, Robert E. "Econometric olicy Evaluation: A Critique." The hillis Curve and the Labor Market (K. Brunner and A. Meltzer, eds.), Vol. 1 of Carnegie-Rochester Conferences in ublic olicy, a sulementary series to the Journal of Monetary Economics. Amsterdam: North-Holland ublishers, Miranda, Mario, and aul Fackler. Comutational Methods in Economics - MATLAB Toolbox. File downloadable from the website htt://www4.ncsu.edu/unity/users//fackler/www/ecg790c/. Newbery, David M., and Joseh E. Stiglitz. "The Theory of Commodity rice Stabilization Rules: Welfare Imacts and Suly Resonses." Economic Journal 89(1979): Williams, Jeffrey C., and Brian D. Wright. Storage and Commodity Markets. New York: Cambridge University ress, Wright, Brian D. "The Effects of Ideal roduction Stabilization: A Welfare Analysis under Rational Exectations." Journal of olitical Economy 87(1979):

18 17 Table 1. Steady-State Simulation Results for Corn, Corresonding to R bean = a No Government Intervention Government Intervention Regime without Regime with re-fair FAIR Regime Random Effects Random Effects Regime FAIR- b FAIR-ay b lanted Acres (0.02) 0.99 (0.03) 1.00 (0.02) 1.00 (0.02) [0.96, 1.00, 1.03] [0.94, 1.00, 1.03] [0.97, 1.00, 1.03] [0.97, 1.00, 1.03] roduction (0.16) 0.99 (0.16) 1.00 (0.16) 1.00 (0.16) [0.74, 1.00, 1.27] [0.73, 0.99, 1.26] [0.74, 1.00, 1.27] [0.74, 1.00, 1.27] Total Suly [0.79, 1.12, 1.46] [0.80, 1.13, 1.51] [0.81, 1.15, 1.59] [0.79, 1.12, 1.47] Current Consumtion (0.10) 0.99 (0.09) 1.00 (0.09) 1.00 (0.10) [0.79, 1.02, 1.12] [0.80, 1.02, 1.06] [0.81, 1.03, 1.06] [0.79, 1.02, 1.13] rivate Storage [0.00, 0.10, 0.34] [0.00, 0.04, 0.19] [0.00, 0.02, 0.17] [0.00, 0.10, 0.34] Government Storage [0.00, 0.00, 0.44] [0.00, 0.00, 0.53] Total Storage [0.00, 0.10, 0.34] [0.00, 0.11, 0.44] [0.00, 0.12, 0.53] [0.00, 0.10, 0.34] Years without Storage (%) rice (0.23) 1.03 (0.21) 1.02 (0.20) 1.02 (0.23) [0.83, 0.97, 1.48] [0.90, 0.97, 1.46] [0.90, 0.96, 1.43] [0.82, 0.96, 1.48] Government Deficiency ayments [0.00, 0.31, 0.40] [0.00, 0.00, 0.09] Government Storage Net Exenditures [ 0.001, 0.00, 0.03] [ 0.002, 0.00, 0.03] Farm Revenues (0.14) 1.28 (0.12) 1.00 (0.13) 1.02 (0.14) [0.80, 1.00, 1.22] [1.04, 1.28, 1.52] [0.78, 1.00, 1.23] [0.81, 1.01, 1.24] a Bold numbers denote mean values, numbers within arenthesis are coefficients of variation, and the three numbers within brackets are, resectively, the 5 ercent quantile, the median (in italics), and the 95 ercent quantile. b FAIR- denotes the scenario where = R and bean = R bean. FAIR-ay denotes the scenario where = bean = 0.