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GTAP Resource #2044

"Using gravity to move Armington - an empirical approach to the small initial trade share problem in general equilibrium models "
by Kuiper, Marijke and Frank van Tongeren

The small shares problem

Most applied general equilibrium models, including GTAP, use a CES-based Armington specification to model bilateral trade flows. Distinguishing traded commodities by origin allows one to model bilateral trade preferences, like those granted in the context of regional trade arrangements. Using CES functions for modeling import demand has a major drawback referred to as the ‘small shares problem. This relates to the fact that producer and consumer incentive prices are calculated as volume weighted shares of prices of domestic and imported goods. However, if trade volumes in the base period are zero (or even close to zero) such weighted averages will not fully reflect the importance of reducing tariffs on imports or other forms of trade protection and domestic agricultural support. Stated simply, if there is no or little trade in the base period, there will likely be no or little trade impact of reducing tariffs - even if that reduction is very large. This implies that general equilibrium models using a CES-based import aggregation function will underestimate the impact of a reduction in trade barriers.

Existing solutions to the small shares problem

To deal with the small shares problem an array of solutions has been proposed in the literature. These range from ad-hoc changes to model parameters (replacing zero trade flows with small numbers, increasing the substitution elasticity between imported goods or aggregating regions or products) ,to structural changes to the model structure. A first take on structural changes is to move to a net trade model. Switching to a net trade model implies that we can no longer observe bilateral trade flows. Given that perfect substitutability only applies to a limited number of selected agricultural (bulk) commodities that can be considered homogenous, and the increasing proliferation of regional trade arrangements, a net trade model does not provide a general solution to the small shares problem.

A second take on structural changes to the model structure is to change the functional form of the import demand function. Several alternatives have been proposed including commitments in the CES function or replacing the CES function with a CRESH or an AIDS function. Replacing the CES function by another specification is appealing from a theoretical point of view but does increase the number of parameters that needs to be estimated, leading to empirical problems when implemented in a disaggregated model. Changing functional form thus also does not provide a general solution to the small shares problem.

A new approach to the small shares problem: shifting the Armington functions

In this paper we develop a new approach to dealing with the small shares problem. We maintain the CES Armington import demand function but shift its market share parameter in accordance with the expected change in trade flows following a change in trade policies. We thus assume that a change in trade barriers induces a change in the ‘import technology’ of a country. This idea of trade liberalization inducing technical change seems implicit in defining the small shares problem by the idea that that trade flows should change more than predicted by functional forms incorporated in the model.

Before considering any modifications to the model structure or its parameters one needs to consider the underlying cause of small initial trade flows. If small trade flows are the result of non-economic factors (for example, distance, language, political barriers) and these non-economic factors do not change in the scenarios analyzed with the model, small shares that remain small are not a problem. If, however, trade barriers are the main reason for small initial trade flows and these are removed in scenarios analyzed with the model the small shares issue needs to be addressed.

To disentangle non-economic causes of small trade flows from trade barriers we use a gravity model to gauge changes in trade flows following a change in trade barriers. Combining trade, tariff and export subsidy data from the GTAP Version 6 database with geographical data supplied by CEPII we estimate a gravity model to simulate bilateral trade flows. We use a theoretically-founded Anderson and van Wincoop style gravity model estimated using a Poisson Pseudo Maximum Likelihood Estimator (PPMLE). The estimated model includes country fixed effects and bilateral data on tariffs, export subsidies and measures of geographical or cultural distance. The absence of country-specific variables like GDP prevents direct inconsistencies between the gravity model and the general equilibrium model. PPMLE provides a consistent and efficient estimation method that allows us to incorporate zero trade flows crucial for the small trade shares problem.

We use the estimated gravity model to simulate the trade flows when trade barriers are reduced.
This provides us with an estimation of the market shares of different trade flows following trade liberalization. We then use the estimated share parameters to shift the Armington import aggregation functions. More specifically we derive a relation between the change in bilateral import price, initial trade shares and trade shares from the gravity model to calibrate a technical change parameter affecting the import technology.

In order to assess the impact of shifting the Armington functions we analyze the impact of full trade liberalization without and with the technology shift. We focus on agricultural sectors that are most strongly protected. We use a modified version of the GTAP model (GTAPEM) that accounts for different substitution possibilities between agricultural sectors. Given the generally high tariffs in agriculture this model allows a better analysis of the changes in production following trade liberalization.

Resource Details (Export Citation) GTAP Keywords
Category: 2006 Conference Paper
Status: Published
By/In: Presented at the 9th Annual Conference on Global Economic Analysis, Addis Ababa, Ethiopia
Date: 2006
Version: 1.0
Created: Kuiper, M. (5/1/2006)
Updated: Kuiper, M. (5/3/2006)
Visits: 5,302
No keywords have been specified.

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