# Whither Armington Trade Models

Abstract: The Armington trade model distinguishes commodities by country of origin, and import demand is determined in a separable two-step procedure. This framework has been applied to numerous international agricultural markets with the objective of modeling import demand. In addition, computable general equilibrium (CGE) models commonly employ the Armington formulation in the trade linkage equations. The purpose of this paper is to test the Armington assumptions of homotheticity and separability with data from the international cotton and wheat markets. Both parametric and nonparametric tests were performed, and the empirical results reject the Armington assumptions. This has important implications for international trade modeling and CGE modeling.

## Summary (2 min read)

### WHITHER ARMINGTON TRADE MODELS?

- Elasticities of import demand are .u~ed commogly to estimate the effects of trade ~arriers and to examine trade policy options.
- The ease of use and flexibility are two reasons why ' the Armington model has been applied so often to international agricultural markets.
- First, nonparametric methods (from Varian 1982 Varian , 1983 ) are used to test (a) whether the data are consistent with a stable system of well-behaved import demand equations and (b) whether Armington restrictions hold.

### Two-Stage Theoretical Models

- In general, a two-stage budgeting procedure assumes that consumers allocate their total expenditures in two stages (Deaton and Muellbauer, 1980b) .
- Weak separability imposes restrictions on consumer behavior#.
- A price change of a commodity in one group affects _the de.mand for_a commodity in another group only through the group income effect.
- In the second stage (equation (3)), given the total amount imported, the importer decides how much to import from each supplier.
- Thus, the Armington framework implies that in the second stage (within-.

### Nonparametric Tests

- The nonparametric approach to demand an 9 lysis uses the results of revealed preference analysis to derive algebraic conditions on demand functions (Varian 1983) .
- The authors can al_so test for the compatibility of data with the existence of a utility function that is homothetic, separable, or both homothetic and separable (as is implied by the Armington model) . .
- Second, for data sets that satisfy GARP the authors can proceed to test compatibility of the ~ata with restrictions on the utility function.
- For the other four wheat _importers and the other four cotton importers separability was rejected for one or more of the source countries.
- Finally, because all of the data violate I:IARP, the test for homothetic separability is redundant.

### Armington Estimates

- This ,model is homogeneous of degree zero in all prices and total expenditure.
- It is not possible in general to impose the theoretical restrictions of symmetry and adding up (e.g. see Deat~n and Muellbauer, 1980b) .
- In four of the cases, separability, homothetic separability, and the Armington model were rejected in all ten cases.
- The full Armington restrictions were rejected in all-ten cases when the models were corrected for first order autocorrelation as well as in the OLS estimation.

### AIDS Model Estimates

- In an AIDS specification (Deaton and Muellbauer 1980a, 1980b) of import demand, the budget sha!e of imports from sourc~ i is given by: (10) The aggregate price deflator in (9) can be approximated by Stone's index from equation ( 6).8.
- Thus, for each import source the authors estimated an AIDS excluding it a~d then tested whether its price had any influence on the included import shares,9 Initially they test this restriction alone without any separability restrictions on sources of imports within the group.
- For Japan the restriction is rejected for both wheat and cotton in the full model including all sources.
- Consider Tables 5 and 6 which summarize results for all countries.

### Synthesis of Results

- Table 7 summarizes the results from the three alternative approaches to testing Armington ~e$trictions on import demand equations for cotton and wheat, A"+" indicates the restriction is not rejected while a "-" indicates the restriction is rejected.
- Separability was rejected iri 8 of 10 countries using the nonparametric approach, all 10 countries using the double-log model, and in 9 of 10 countries using the AIDS mod~!.
- These necessary conditions are relatively weak restrictions compared to the Armington separability restrictions.
- On this criterion the results are quite unequivocal.
- _With all three approaches and in each country the Armington restrictions were _ _ comprehensively rejected.

### Implications

- . Armington model estimates are commonly used in counterfactual policy simulations.
- In such contexts, the acid test might not be whether the Armington restrictions are rejected by the data but, rather, whether the resulting elasticity estimates are significantly biased.
- _We can P!Ovide a partial answer to this :question.the authors.the authors.
- When the omitted prices are p~ices of substitutes (posit_ive cross-elasticities), the own-price parameter estimate will be positively biased so that the own-price elasticities will be underestimated (i.e. less negative).
- 10 This argument is relatively straightforward in the context of the double-log model about which the authors have already expressed their reservations.

### Con cl us ions

- This paper tested the assumptions of the Armington trade model in the context of the international cotton-and wheat markets.
- The Armington model is comprehensively rejected wit~ data from ,.the five leading importing countries for each good, using thre~ alternative testing approaches.
- By analogy doubt is raised as to whether the Armington restrictions are appropriate for other goods and in other applications such as CGE modeling.
- In order to make consumer models tractable these separability assumptions are frequently made.
- "\Yhile this does not lead to biased p~rameter estimates, it might lead to biased standard errors and biased test results.

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### Cites background from "Whither Armington Trade Models"

...For example, Winters (1984), and Alston et al. (1990) argue that the functional form is too restrictive and that the nonhomothetic, AIDS specification is preferable....

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...This specification was first proposed by Paul Armington in 1969 and has since become known as the "Armington approach" to modeling import demand....

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...This specification was first proposed by Paul Armington in 1969 and has since become known as the "Armington approach" to modeling import demand. However, it has been widely criticized in the literature. For example, Winters (1984), and Alston et al....

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