Foreig Price Risk ad Homogeeous Commodity Imports: A Focus o Soybea Demad i Chia Adrew Muhammad, Ph.D. Seior Research Ecoomist Ecoomic Research, USDA Iteratioal Agricultural Trade Research Cosortium December 11-13, 2011 St. Petersburg, Florida The views expressed here are those of the author(s), ad may ot be attributed to the Ecoomic Research Service or the U.S. Departmet of Agriculture.
Overview This study provides a theoretical foudatio ad model that relates import price risk to the allocatio of a homogeeous commodity across exportig coutries. A differetial approach to expected utility theory ad firm demad is used to derive a empirical model that accouts for the effects of price risk o the demad for a commodity disaggregated by source. My focus is the soybea market i Chia, which is the largest destiatio market for global soybea exports.
Why is price risk importat? I purchasig a commodity from multiple coutries, firms are diversifyig away the price risk associated with relyig o a sigle low-cost exporter. Dudley (1983) - whe iput prices are ucertai, it is geerally optimal for a firm to remai diversified i its choice of suppliers eve whe prices differ across sources. Wolak ad Kolstad (1991) - import allocatio is aalogous to asset allocatio where risk maagemet behavior could explai why a homogeeous commodity is sourced from multiple coutries.
Past Research Price risk ad import demad, aggregate trade flows: Aderso ad Garcia, 1989; Pick, 1990; Appelbaum ad Kohli, 1997, 1998; Lagley et al., 2000; Cho, Sheldo ad McCorristo, 2002; Appelbaum ad Woodlad, 2010. Import allocatio ad price risk: Wolak ad Kolstad (1991) (Japaese steam-coal imports), ad Seo (2001) (Chiese wheat imports).
100.00 Chia s Soybea Imports: Ja. 2005-Dec. 2009 (billio kilograms) 5.00 90.00 4.50 Quatity Share (percet) 80.00 70.00 60.00 50.00 40.00 30.00 20.00 4.00 3.50 3.00 2.50 2.00 1.50 1.00 Total Imports (billio kilograms) 10.00 0.50 0.00 2005 2006 2007 2008 2009 Argetia Brazil Uited States 0.00 Source: World Trade Atlas Database
Chia s Soybea Prices by Exporter: Ja. 2005-Dec. 2009 ($US per kilograms) 0.70 0.60 0.50 0.40 0.30 0.20 2005 2006 2007 2008 2009 Brazil Argetia U.S. Source: World Trade Atlas Database
0.20 Chia s Soybea Prices by Exporter: Ja. 2005-Dec. 2009 (log differeces) 0.15 0.10 0.05 0.00-0.05-0.10-0.15-0.20-0.25-0.30 2005 2006 2007 2008 2009 Brazil Argetia U.S. Source: World Trade Atlas Database
Import allocatio as the first stage of a expected utility problem R : et reveue from outputs ad domestic resources. p i ad q i deote the price ad quatity of a commodity from the ith coutry (i = 1, 2 ). The optimal allocatio of q is the solutio to the followig: [ pq pq ] Max U R E( ), V( ) q s.t. Q = ιq, q 0 The Lagragia for the utility maximizatio problem is Λ= U( R pqqωq, ) + λ( Q ι q) The first order coditio with respect to the ith import (q i ) is Λ Λ = = Up+ 2U qσ + qσ λ = 0 ( 2 ) i 1 i 2 i i i i qi
Import allocatio equatio i geeral form The optimizatio problem results i a system of import demad equatios q i = q i (Q, p 1, p 2,, p, σ, σ,, σ ) Similar to the differetial approach (Theil, 1977; Theil, 1980; Laitie, 1980; Theil ad Clemets, 1987) q q q dq dq dp d With some maipulatio i i i 2 i = + + σ 2 Q = 1 p = 1 σ q log q log q sd q d Q s d p s d i i i 2 i log i = log + i log + i logσ 2 Q = 1 log p = 1 logσ 2 1 2 2 2 s i = q i / Q is the share of imports from coutry i i total imports.
Similar to the differetial approach (Theil, 1977; Theil, 1980; Laitie, 1980; Theil ad Clemets, 1987) Solvig for the price ad variace effects q log q log q sd q d Q s d p s d i i i 2 i log i = log + i log + i logσ 2 Q = 1 log p = 1 logσ log qi i log qi log Q log λ = u γ E u + log p log Q log λ log p i ψ1 = 1 log q log q log Q log λ logσ log log λ logσ i i i i = u φ 2 V u ψ2 + 2 = 1 Q
Differetial Import Allocatio (DIA) Model 12 * 2 it it = θi t + πi t + νi σ t + δi m + εit = 1 = 1 m= 1 s q Q p d x t = l(x t ) l(x t-1 ) d log x t s = 0.5( s + s ) θ = q i it it it * t i= 1 it it Q = s q i / Q 1 The DIA model is similar to the Rotterdam model with exceptio of the followig: The average ad margial share (s i ad θ i ) are defied i terms of quatity ad ot expeditures. Allocatio is based o the aggregate quatity ad ot aggregate expeditures; Import demad is determied by price expectatios ad risk, ad ot actual prices.
Differetial Import Allocatio (DIA) Model 12 * 2 it it = θi t + πi t + νi σ t + δi m + εit = 1 = 1 m= 1 s q Q p d Addig up (costrait coditio): θ = 1; π = 0; ν = 0; δ = 0 i= 1 i i= 1 i i= 1 i i= 1 i Negativity: π < 0 i Risk adverse: ν < 0 i ii ii Homogeeity: Symmetry: π i π = 1 i = π i = 0 Risk Neutrality: ν i = 0 i
Soybea Imports i Chia Chia is the largest soybea importig coutry i the world. Accordig to the Uited Natios, global soybea trade is valued at $28.1 billio (2009), where Chia accouts for about two-thirds of this total. Chia is also a large soybea-producig coutry. Domestic soybeas are o-biotech ad primarily used to produce food products. Imported soybeas are categorized as biotech ad ca oly be used to produce soybea meal ad oil. Mothly data are used for estimatio (Jauary 2005 December 2009) (World Trade Atlas). Durig this period, Argetia, Brazil, the Uited States accouted for about 99% of total soybea imports ad separately accouted for 21.1%, 33.3%, ad 44.2%, respectively, o average.
Multivariate ARCH Procedure To obtai the coditioal expectatio ad variace of import prices, the followig autoregressive equatio is estimated assumig a Multivariate ARCH(2) process. p = α + Α p + Α z + Α z + ε t 0 1 t 1 2 t 3 t 1 t ˆ t = 0 + 1 t 1 t 1 1+ 2 t 2 t 2 2 Ω Β Βε ε Β Βε ε Β
Multivariate ARCH(2) Estimates: March 2005-Dec. 2009 0.050 0.045 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000 2005 2006 2007 2008 2009 Brazil Argetia U.S.
Likelihood ratio tests results Models Log-likelihood Value LR Statistic Restricted parameters P-value Urestricted 96.116 Homogeeity 92.946 6.339 2 0.042 Symmetry 88.730 8.432 1 0.004 Ow-risk* 76.771 32.351 4 0.000 Risk Neutrality* 73.763 38.366 6 0.000 * Compare to the symmetry costraied model.
Import demad estimates for Chia s soybea imports Coutry Margial Price effects π i Risk effects ν i share θ i Brazil Argetia U.S. Brazil Argetia U.S. Brazil 0.487-0.027 0.064-0.037-0.034 0.022-0.042 (0.057) a (0.007) a (0.015) a (0.020) (0.012) a (0.036) (0.022) b Argetia 0.238 0.014-0.154 0.140 0.037-0.070 0.061 (0.046) a (0.006) b (0.012) a (0.016) a (0.010) a (0.029) b (0.017) a U.S. 0.276 0.013 0.090-0.103-0.003 0.048-0.018 (0.026) a (0.009) (0.019) a (0.024) a (0.015) (0.044) (0.027) Asymptotic stadard errors are i paretheses. The R 2 for Brazil, Argetia, ad the Uited States are 0.89, 0.95, ad 0.76, respectively. a & b deote the 0.01 ad 0.05 sigificace level, respectively.
Seasoality estimates Brazil Argetia U.S. Ja. 0.024-0.023-0.001 Feb. 0.013 0.124-0.137 March -0.174 * -0.085 0.259 * April 0.371 * -0.115 * -0.256 * May 0.134 * 0.156 * -0.290 * Jue -0.036 0.284 * -0.248 * July 0.022-0.037 0.016 Aug. 0.041 0.050-0.091 Sep. -0.014-0.091 * 0.106 Oct. -0.106-0.012 0.118 Nov. -0.162 * -0.106 * 0.268 * Dec. -0.178 * -0.138 * 0.316 * Asymptotic stadard errors are i paretheses. * deotes a sigificace level 0.05.
Import demad elasticities for Chia s soybea imports Total Ow/Cross Price Ow/Cross Risk Coutry Import Brazil Argetia U.S. Brazil Argetia U.S. Brazil 1.366* -0.075* 0.179* -0.104-0.096* 0.062-0.120* Argetia 1.061* 0.063* -0.687* 0.624* 0.167* -0.313* 0.273* U.S. 0.657* 0.030 0.214* -0.244* -0.008 0.114-0.043 Asymptotic stadard errors are i paretheses. * deotes a sigificace level 0.05.
Summary/Coclusio Overall, price risk (uexplaied volatility) is a importat determiat of Chia s soybea demad by source, eve whe price ad seasoality effects are accouted for. Imports from Brazil ad Argetia are decreasig i owprice risk which could idicate risk averse behavior. No risk effects were sigificat for the U.S. While prices i Brazil were the most volatile, imports from Argetia were the most sesitive to ow-price risk. Price risk i competig coutries have a positive effect o Argetia, but ot the reverse.