Appendix E: Economic Model

Model Overview

Chapter 8 uses an industry-specific partial equilibrium model of the global rice market to simulate the effects of country-specific policies on the industry and consumers in the United States and other major rice-producing and -consuming countries. The prospective model is calibrated to 2023 trade data with two types of rice (aromatic and nonaromatic), two stages of processing (paddy and milled rice), and 185 countries aggregated into 18 country groups (16 individual countries and two aggregate groups). The model is used to analyze the impacts of tariffs, export bans, tariff-rate quotas (TRQs), export charges, minimum support prices, and government-to-government contracts.[1]

Table E.1 List of countries included in the rice model

Group	Countries
Individual countries in the model	Bangladesh, Brazil, Burma, Cambodia, China, India, Indonesia, Japan, Pakistan, Paraguay, Philippines, South Korea, Thailand, United States, Uruguay, Vietnam
Aggregate groups	Other developed countries, other developing countries

Source: Compiled by the USITC.

Supply Structure

In the following three sections, the subscripts $i$ , $j$ , $k$ , and $f$ denote the type of rice (aromatic or nonaromatic), exporting country, importing country, and factor input in the production of paddy rice, respectively.

The model assumes a perfectly competitive global rice market where each country produces a unique variety of rice with characteristics that differentiate it from rice produced in other countries. Four countries—India, Pakistan, Thailand, and Vietnam—produce aromatic rice in addition to nonaromatic rice and produce a unique variety of each type. The production process consists of two steps: rice farming and milling (processing). Trade can occur after either step in the production process. That is, rice can be traded as paddy rice and then processed in the destination country or processed in the source country and traded as milled rice. The supply of paddy rice in metric tons ( $Q_{i j}$ ) from each country is determined by the equation below.

$Q_{i j} = α_{i j} {(p_{i j} (1 + ω_{i j}))}^{θ_{i j}}$

$p_{i j}$ is the producer price of paddy rice type $i$ in country $j$ ; $ω_{i j}$ are general ad valorem production subsidies for rice type $i$ produced in country $j$ ; and $θ_{i j}$ is the elasticity of supply for paddy rice. The calibrated supply shift parameter ( $α_{i j}$ ) captures country-specific factors for each rice type that shift the supply curve.

In the model, eight factor inputs are used in paddy rice farming: fertilizer, pesticides, energy, water, seed, land, labor, and capital. The quantity of each factor input $f$ used to produce one unit of paddy rice quantity ( $Q_{i j}$ ) in country $j$ is represented by $g_{i j f}$ . The price of each unit of factor input $f$ in country $j$ used in the farming of rice type $i$ is $w_{i j f}$ . The first equation below represents each factor input’s share of the total cost of production of paddy rice, where $\int_{f = 1}^{F} ψ_{i j f} = 1$ and $F$ is the total number of factors used in the production of paddy rice. The cost shares of factor input $f$ in the production of paddy rice type $i$ in country $j$ ( $ψ_{i j f}$ ) comes from the Cobb-Douglas production function for paddy rice in the second equation below.

$ψ_{i j f} = \frac{w_{i j f} g_{i j f}}{(\sum_{f = 1}^{F} w_{i j f} g_{i j})}$

$Q_{i j} = A \sum_{f = 1}^{F} g_{i j f}^{ψ_{i j f}}$

In the model, the processing of paddy rice into milled rice is represented by the Leontief production function with two inputs, paddy rice ( $Q_{i j}$ ) and all the value-added resources used in the milling process, $K_{i j}$ in the equation below.

$m_{i j} = m i n \{λ_{i j} Q_{i j}, K_{i j}\}$

$h_{i j} = p_{i j} Q_{i j} + ν_{i j} K_{i j}$

$λ_{i j}$ is the milling quantity recovery rate for rice type $i$ in country $j$ , and the quantity of milled rice produced is $m_{i j}$ . $h_{i j}$ is the total cost of milling, and $ν_{i j}$ is the fixed value added to paddy rice type $i$ of milling in country $j$ .

Demand Structure

The model has a nested constant elasticity of substitution (CES) demand structure. Consumers choose the types and sources of rice among which to allocate their total expenditure on rice. The consumers’ decision is determined by maximizing their CES utility function subject to their budget constraint. The aggregate utility function for country $k$ is represented by the following three equations where $J$ and $I$ are the total number of source countries and rice types, respectively.

$m a x U_{k} (q_{i j k}) = \sum_{i = 1}^{I} {(γ_{i k} u_{i k}^{\frac{ϕ - 1}{ϕ}})}^{\frac{ϕ}{1 - ϕ}}$

$s . t u_{i k} = \sum_{j = 1}^{J} {(β_{i j k} q_{i j k}^{\frac{σ - 1}{σ}})}^{\frac{σ}{1 - σ}}$

$a n d s . t . E_{k} = \sum_{i = 1}^{I} \sum_{j = 1}^{J} d_{i j k} q_{i j k}$

In the above equations, $β_{i j k}$ is the calibrated demand preference parameter of consumers for the rice type $i$ imported by country $k$ from country $j$ and $γ_{i k}$ is the calibrated demand preference parameter for country composite rice type $i$ in country $k$ . $σ$ is the elasticity of substitution between sources of each rice type $i$ , and $ϕ$ is the elasticity of substitution between nonaromatic and aromatic types of rice. The budget constraint for country $k$ is that total expenditure ( $E_{k}$ ) must equal the quantity of rice supplied ( $q_{i j k}$ ) multiplied by the delivered price of rice ( $d_{i j k}$ ) type $i$ from source country $j$ to destination country $k$ . The delivered prices are a function of the producer prices, policy-induced price shifters, and location of paddy rice milling defined by the equation below.

$d_{i j k} = ((1 - μ_{i j k}) (\frac{p_{i j}}{λ_{i j}} + ν_{i j}) + μ_{i j k} (\frac{p_{i j}}{λ_{i k}} + ν_{i k})) (1 + τ_{i j k}) (1 - δ_{i k}) (1 + r_{i j k}) (1 + ξ_{i j k})$

All policy-induced price shifters are included as ad valorem rates. $τ_{i j k}$ is the tariff rate applied by country $k$ to imports from country $j$ of rice type $i$ ; $δ_{i k}$ is the consumption subsidy in country $k$ for rice type $i$ ; and $ξ_{i j k}$ are the export charges applied by country $j$ on its exports to country $k$ of rice type $i$ . The quota rent rate ( $r_{i j k}$ ) is the cost of quota policies, including export quotas and import quotas. The quota policies cause a discrepancy between supply and demand that can result in higher prices. The quota rent rate behaves like a tariff except, instead of the government receiving revenue, the exporting producers restricted by the quota receive economic rents from higher prices. The rent rate is endogenous in the model and is required for all counterfactuals, including those that do not directly simulate changes to quota policies. All counterfactuals shift the equilibrium and affect the size of the discrepancy between supply and demand caused by the import and export quotas.

Outside of the policy-induced price shifters, delivered prices also include differences depending on where the paddy rice is processed. $μ_{i j k}$ is the share of rice type $i$ exported from country $j$ to country $k$ that is paddy rice; $λ_{i j}$ and $λ_{i k}$ are the milling recovery rates of rice type $i$ for countries $j$ and $k$ , respectively; and $ν_{i j}$ and $ν_{i k}$ are the fixed milling costs of paddy rice in countries $j$ and $k$ , respectively.

The demand function for rice type $i$ exported from country $j$ to country $k$ implied by country $k$ ’s utility function is defined below.

$q_{i j k} = E_{k} {(Z_{k})}^{η + ϕ} {(P_{i k})}^{σ - ϕ} {(d_{i j k})}^{- σ} β_{i j k} γ_{i j k}$

The parameter $η$ is the price elasticity of total industry demand, and the CES price index in the inner nest for the two different composite rice types in country $k$ ( $P_{i k}$ ) is represented by the following equation.

$P_{i k} = {(\sum_{j = 1}^{J} β_{i j k} {(d_{i j k})}^{1 - σ})}^{\frac{1}{1 - σ}}$

The CES price index in the outer nest ( $Z_{k}$ ), which represents the average consumer price for all rice in country $k$ , is defined below.

$Z_{k} = {(\sum_{i = 1}^{I} γ_{i k} {(P_{i k})}^{1 - ϕ})}^{\frac{1}{1 - ϕ}}$

The global demand for each paddy rice type $i$ supplied by country $j$ is represented by the following equation, where $K$ is the total number of importing countries.

$G_{i j} = \sum_{k = 1}^{K} \frac{q_{i j k}}{(1 - μ_{i j k}) λ_{i j} + μ_{i j k} λ_{i k}}$

The market clearing condition is defined by the following equation.

$G_{i j} = Q_{i j}$

Some countries in the model have import quotas or export controls. In these cases, the bilateral trade flows that are subject to the quotas must also satisfy the market clearing conditions in the equations below. $T_{i j k}$ are the binding TRQ quantities applied by country $k$ to imports of rice type $i$ from country $j$ , and $C_{i j k}$ are the quantitative export controls applied by country $j$ to its exports of rice type $i$ to country $k$ . In certain instances (e.g., India exporting to Japan), one country has an export quota and the other has an import quota. In these cases, the model assumes that the export control is binding.[2]

$T_{i j k} = q_{i j k}$

$C_{i j k} = q_{i j k}$

Data Description

The model uses producer prices and bilateral trade in quantities as the main inputs along with many parameters. The bilateral trade data come from the Global Trade Analytics Suite (GTAS).[3] The 6-digit level of the Harmonized Commodity Description and Coding System (HS) includes four categories of rice (table E.2).

Table E.2 Harmonized Commodity Description and Coding System (HS) codes and descriptions for rice

HS 6-digit code	Description
100610	Rice in the husk (paddy or rough)
100620	Husked (brown) rice
100630	Semi-milled or wholly milled rice, whether or not polished or glazed
100640	Broken rice

Source: S&P Global, GTAS database, accessed August 30, 2024.

The parameter $μ_{i j k}$ , which represents the share of total rice trade that is paddy rice (described by the HS as rice in the husk), is calculated from the trade data by dividing the quantity of trade classified under HS code 100610 in metric tons by the total rice traded. Once the share parameter is determined, all rice trade is aggregated into one HS 4-digit group (1006). Additionally, the model uses production data in combination with the trade data to calculate domestic shipments of each rice type ( $q_{i, j = k, k}$ ). The production data come from the U.S. Department of Agriculture (USDA) Production, Supply and Distribution (PSD) Online database.[4] Domestic shipments are calculated by subtracting each country’s exports from its production.[5] Four countries examined for this report produce aromatic rice: India, Pakistan, Thailand, and Vietnam. Neither the PSD Online production data nor the HS classifications for trade data disaggregate aromatic and nonaromatic rice. To disaggregate the data, the model uses share parameters from the RiceFlow model used in the 2015 U.S. International Trade Commission (Commission) report on rice.[6] These parameters provide the share of production in each country that is aromatic and the share of each bilateral trade flow that is aromatic.[7] Where more recent data were available, these shares were updated using country-specific information and sources.[8] The table below provides the aromatic share of production data that were used in the model for this report.[9]

Table E.3 Aromatic share of production data

Country	Aromatic share of production	Source	Year of data
India	0.096	India Grains and Feed Annual Report	2023
Pakistan	0.350	RiceFlow	2013
Thailand	0.350	S&P Export Data and the Government of Thailand Office of Agricultural Economics	2023
Vietnam	0.20	United States Department of Agriculture, United States government official	2023

Source: Durand-Morat and Wailes, RiceFlow, accessed various dates; USDA, accessed various dates; Government of Thailand Office of Agricultural Economics, accessed March 2024; interview with foreign government official, accessed September 20, 2024; S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024.

The PSD Online production data provide the production of both paddy and milled rice for each country. The milling quantity recover rates ( $λ_{i j}$ and $λ_{i k}$ ) are calculated by dividing each country’s milled production by its paddy rice production.

Producer prices for nonaromatic paddy rice data come from the Food and Agriculture Organization of the United Nations (FAO) FAOSTAT database and data from the RiceFlow model.[10] The annual producer prices of paddy rice are only available for the 2022 calendar year, so the model proxies the 2023 producer price data with the 2022 data. The table provides the prices, source, and year of data.

Table E.4 Producer price of rice data

In dollars; FAO = Food and Agriculture Organization; — (em dash) = not applicable; mt = metric tons.

Trading partner	Nonaromatic producer price ($/mt)	Source nonaromatic	Year of nonaromatic data
Bangladesh	220.40	FAO/RiceFlow (imputed value)	—
Brazil	279.10	FAO	2022
Burma	179.22	FAO/RiceFlow (imputed value)	—
Cambodia	267.17	FAO/RiceFlow (imputed value)	—
China	413.10	FAO	2022
India	222.96	FAO/RiceFlow (imputed value)	—
Indonesia	392.39	FAO	2022
Japan	1413.20	FAO	2022
Pakistan	735.10	FAO	2022
Paraguay	354.00	FAO/RiceFlow (imputed value)	—
Philippines	320.10	FAO	2022
South Korea	1803.90	FAO	2022
Thailand	299.20	FAO	2022
United States	427.69	FAO	2022
Uruguay	235.00	FAO	2022
Vietnam	311.40	FAO	2022
Developed group	331.35	FAO (average of developed)	2022
Developing group	303.81	FAO (average of developing)	2022

Source: FAO, FAOSTAT database, “Producer Price”, accessed various dates; USITC imputed value using data from FAO, “Producer Price,” FAOSTAT database and Durand-Morat and Wailes, RiceFlow, accessed various dates.

Not all individual countries have producer prices available in the FAOSTAT database. For those without producer price data available, producer prices from the 2015 Commission report are used and scaled up by the average price increase from 2015 to 2022 for the countries where 2022 producer price data are available. The producer price of aromatic rice is calculated by scaling up the 2022 producer prices of nonaromatic rice from FAOSTAT, using the relative difference between aromatic and nonaromatic rice prices in the 2015 Commission report that used the RiceFlow model.[11] The producer prices for the aggregated developing-country and developed-country groups are the simple average of FAO producer prices in the developed and developing countries.

On the supply side, the model uses the factor input shares of total production costs ( $ψ_{i j f}$ ) as inputs. These shares are from various country-specific sources, and where no cost-of-production data more recent than 2013 are available, the cost shares from the 2015 RiceFlow model are used.[12] The table below lists the countries, sources, and year of the cost shares used.

Table E.5 Sources and year of most recent cost shares of production data

Trading partner	Source	Year
Bangladesh	RiceFlow	2013
Brazil	RiceFlow	2013
Burma	RiceFlow	2013
Cambodia	RiceFlow	2013
China	RiceFlow	2013
India	Government of India	2021
Indonesia	Khoiriyah et al. (2023)	2023
Japan	Government of Japan Ministry of Agriculture, Forestry and Fisheries	2024
Pakistan	Government of Pakistan	2022
Paraguay	RiceFlow	2013
Philippines	RiceFlow	2013
South Korea	Statistics Korea	2024
Thailand	Fakkong and Suwanmaneepong (2016)	2016
United States	United States Department of Agriculture	2023
Uruguay	Asociación Cultivadores de Arroz	2023
Vietnam	RiceFlow	2013
Developed Group	RiceFlow	2013
Developing Group	RiceFlow	2013

Source: Durand-Morat, Alvaro and Weiles, RiceFlow, accessed various dates; USDA, ARMS, accessed August, 2024; Government of India, “Cost of Cultivation/Production Estimates,” accessed April 6, 2024; Government of Pakistan, “Rice Paddy Policy Analysis for 2022–23 Crop,” accessed October 29, 2024, Fakkong and Suwanmaneepong (2016), “Determinants of Profitability of Rice Farming in Peri-Urban Area, Bangkok, Thailand,” accessed various dates; Asociación Cultivadores de Arroz, “Costos productivos,” accessed various dates.

The model contains five elasticity values: the Armington elasticity of substitution between country sources within the two rice composites ( $σ$ ), elasticity of substitution between the two rice composites ( $ϕ$ ), elasticity of total industry demand ( $η$ ), elasticity of supply for paddy rice ( $θ_{i j}$ ), and the price elasticity of supply for land ( $ϵ_{i j}$ ). The elasticity values are listed in the table below.

Table E.6 Elasticity estimates

Elasticity	Value	Source
$σ$	5	GTAP
$ϕ$	3	Commission estimate, assuming the elasticity of substitution between composites will be less than within composites
$η$	−1	Commission estimate
$ϵ_{i j}$	0.5	Commission estimate
$θ_{i j}$	Varies	Calibrated by the model in the section below

Source: Aguiar, A., Chepeliev, M., Corong, E., & van der Mensbrugghe, D. (2023). “The Global Trade AnalysisProject (GTAP) Data Base: Version 11,” accessed August 2023.

The model also uses tariff data from the United Nations Conference on Trade and Development Trade Analysis Information System accessed through the World Integrated Trade Solution database.[13] Average tariff levels between pairs of countries are computed as a simple average of the ad valorem equivalent tariffs for all Harmonized Tariff Schedule of the United States (HTS) 8-digit products relating to rice.[14] Most-favored-nation tariff rates are used by default, but in cases where two countries have a trade agreement, the preferential rate is used instead.

The tariff rates used for the developed- and developing-country groups are the trade-weighted average of the tariff rates for the countries included in the groups. These tariff rates are in turn calculated as a simple average of tariffs applied by a given developed or developing country at the HTS 8-digit level. For the European Union and Colombia, which have TRQ policies, ad valorem equivalent rates are calculated by computing the total revenue from out-of-quota imports and dividing this revenue by the total value of imported rice.

The TRQ information used for Japan in the model comes from USDA Global Agricultural Information Network reports.[15] The model does not use current production subsidies because of a lack of concrete data for countries included in the model. The information on India’s export ban and government-to-government contracts comes from governmental notices.[16]

For the quantitative assessment of food security, the model produces the change in daily caloric intake using the change in quantity of rice consumption. The model uses this change to calculate the percentage change in the USDA Economic Research Service calorie gap index for the individual developing countries in the model and the developing-country aggregate group.[17]

Model Calibration

The model uses the baseline data and exogenous parameters described in the section above to calibrate some of the supply and demand parameters and elasticities. The factor input cost shares of production, including the cost share of land rents ( $χ_{i j}$ ), are exogenous and remain constant. Additionally, all elasticities are exogenous and remain constant in the model, other than the elasticity of supply for paddy rice, which is calibrated according to the following equation. $ϵ_{i j}$ is the elasticity of supply of land for paddy rice production.

$θ_{i j} = \frac{1 - χ_{i j} + ϵ_{i j} χ_{i j}}{χ_{i j}}$

In the following equations, the superscript “ $*$ ” denotes initial values. The supply initial shift parameter ( $α_{i j}^{*}$ ) is calibrated according to the equation below.

$α_{i j}^{*} = q_{i j}^{*} {(p_{i j}^{*} (1 + ω_{i j}^{*}))}^{- θ_{i j}}$

The model uses initial delivered prices, which are a function of data inputs, including the producer prices, milling quantity recovery rates and costs, and the costs imposed by government policies, to calibrate the inner nest demand shift parameter ( $β_{i j k}$ ).

$β_{i j k} = \frac{{(\frac{d_{i j k}^{*}}{d_{i, j = k, k}^{*}})}^{σ} q_{i j k}^{*}}{q_{i, j = k, k}^{*}}$

Countries in the model do not always have domestic production for aromatic rice. When this is the case, the demand shift parameter above becomes undefined. In these cases, the model normalizes the demand shift parameter around aromatic rice imports from India rather than the domestic shipments of aromatic rice, which would be zero for countries with no aromatic rice production.

The outer nest demand shift parameter is calibrated according to the following equation. Subscripts “ $i = n$ ” and “ $i = a$ ” denote nonaromatic and aromatic rice types, respectively.

$γ_{i k} = \frac{(\sum_{j = 1}^{J} v_{i = a, j k}^{*}) {(\frac{P_{i = a, k}^{*}}{P_{i = n, k}^{*}})}^{ϕ - 1}}{\sum_{j = 1}^{J} v_{i = n, j k}^{*}}$

The aggregate expenditure on rice by each country $k$ is calibrated using the equation below. The model assumes that expenditure on rice remains constant.

$E_{k} = q_{i j k}^{*} {(Z_{k}^{*})}^{- η - ϕ} {(P_{i = n, k}^{*})}^{ϕ - σ} {(d_{i = n, j = k, k}^{*})}^{σ}$

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[1] In addition to the policies modeled in this report, the model could be used to analyze the impacts of consumption and production subsidies. These production and consumption subsidy policies are not used for counterfactual simulations because of a lack of consistent data on the value of the subsidies for the countries in the model.

[2] In simulation 6, we do not remove the out-of-quota tariff rate to isolate the effects of strictly import tariff policies.

[3] S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024.

[4] USDA, FAS, PSD Online database, “Grains,” accessed various dates.

[5] The annual trade data are based on the calendar year, and the production data are based on the marketing year, which varies by country. The model assumes that the marketing year dates align with the calendar year dates for all countries.

[6] USITC, Rice: Global Competitiveness, 2015; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model,”, July 2010.

[7] For countries that do not produce aromatic rice, the aromatic share of production is set to zero. For countries that do not import aromatic rice from a specific country, the aromatic share of bilateral trade is set to zero.

[8] S&P Global, Total exports, HS heading 1006, rice, accessed August 30, 2024; Government of Thailand, Office of Agricultural Economics, Agricultural Statistics of Thailand 2023, March 2024; USDA, FAS, Grain and Feed Annual: India 2024, March 29, 2024; U.S. government official, interview by USITC staff, September 20, 2024.

[9] The aromatic shares of each bilateral trade flow are not reported in this appendix because of the large number of shares.

[10] FAO, FAOSTAT database, “Producer Prices,” accessed various dates; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model,” July 2010.

[11] USITC, Rice: Global Competitiveness, 2015.

[12] Kookkaew, “Cost and Return on Investment,” January 2019, 91; Government of India, MAFW, “Cost of Cultivation/Production Estimates,” April 6, 2024; ACA, “Costos productivos,” December 2023, 30; BRRI, “Estimation of Costs and Returns,” November 2023, 245; Government of Pakistan, “Rice Paddy Policy Analysis for 2022–23 Crop,” accessed October 29, 2024, 13; Durand-Morat and Wailes, “RiceFlow: A Multi-Region, Multi-Product, Spatial Partial Equilibrium Model of the World Rice Economy,” July 2010; Fakkhong and Suwanmaneepong, “Determinants of Profitability of Rice Farming in Peri-Urban Area, Bangkok, Thailand,” 2016; 통계청 [Statistics Korea], “2023년산 논벼(쌀) 생산비조사 결과 [Results of the 2023 Rice Paddy Production Cost Survey],” December 12, 2024; MAFF, “農産物生産費統計 [Agricultural Production Cost Statistics],” December 12, 2024; Khoiriyah et al., “Analyzing The Cost of Paddy Rice Labor in Indonesia,” August 19, 2023, 195–198; USDA, ERS and NASS, “Agricultural Resource Management Survey (ARMS),” accessed August, 2024.

[13] WITS database, “Tariff-View and Export Raw Data,” accessed August 16, 2024.

[14] As a robustness check, tariffs were also computed as a trade-weighted average of the rates between two countries. The use of this alternative tariff computation method did not have any noticeable impact on results.

[15] USDA, FAS, Japan: Grain and Feed Annual, March 20, 2024.

[16] Kumar Sarangi, written letter to the government of India, Ministry of Commerce and Industry, October 18, 2023.

[17] USDA, FAS, “Global Food Security Snapshot,” accessed various dates.