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Alternative Methods forEstimating Price Elasticities ofImportsRigoberto A. Lopez aa Department of Agricultural and ResourceEconomics, University of Connecticut, Storrs, CT,06269-4021, USAPublished online: 12 Oct 2008.

To cite this article: Rigoberto A. Lopez (2001): Alternative Methods for EstimatingPrice Elasticities of Imports, Journal of International Food & Agribusiness Marketing,11:4, 21-31

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Alternative Methodsfor Estimating Price Elasticities

of Imports

Rigoberto A. Lopez

ABSTRACT. This article compares three commonly-used methods forestimating import price elasticities: (1) trade-weighted price elasticities ofdomestic demand and supply along with price transmission; (2) directestimates based on ad hoc import demands; and (3) Armington modelestimates. Using data from El Salvador’s grain markets (white maize,red beans, and rice), the results indicate that the second method pro-vides the most reliable estimates and that the Armington procedure maynot be appropriate for estimations of this type. However, the first meth-od offers the best guesstimates to assess potential rather than historicalimport response as trade is liberalized. [Article copies available for a feefrom The Haworth Document Delivery Service: 1-800-342-9678. E-mail address:<getinfo@haworthpressinc.com> Website: <http://www.HaworthPress.com>� 2000 by The Haworth Press, Inc. All rights reserved.]

KEYWORDS. Import demand, import price elasticity, trade analysis,El Salvador, basic grains

Rigoberto A. Lopez is Professor, Department of Agricultural and Resource Eco-nomics, University of Connecticut, Storrs, CT 06269-4021 (E-mail: rlopez@canr.uconn.edu).

The author is grateful to the Crecer-El Salvador project under partnership be-tween Chemonics International and the U.S. Agency for International Development.Special thanks to Hugo Ramos and to the staff of the Ministry of Agriculture andLivestock of El Salvador for their assistance in data collection. The author, however,is solely responsible for the content of the paper and any remaining errors.

This paper is Scientific Contribution No. 1949 of the Storrs Agricultural Experi-ment Station.

Journal of International Food & Agribusiness Marketing, Vol. 11(4) 2000� 2000 by The Haworth Press, Inc. All rights reserved. 21

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INTRODUCTION

Given the ongoing wave of trade liberalization, one of the mostimportant issues is the responsiveness of import flows to pricechanges; that is, the price elasticity of imports. There are numerousstudies dealing with the subject of estimating import elasticities (seeCarter and Gardiner, 1988, for a review), given its importance inpolicy making decisions and in understanding and anticipatingchanges in import flows as domestic and world conditions change.

In this article, three methods are considered: (1) trade-weightedprice elasticities of domestic supply and demand; (2) direct estimatesbased on import demand functions; and (3) an Armington (1969)model. The first is the simplest, as it can readily be calculated fromexisting reliable estimates of domestic elasticities of demand and sup-ply and thus can provide quick answers to those needing import elasti-cities. In addition, rather than being based on historical import re-sponse, this approach can offer a fresh insight into likely importresponse as imports are liberalized. The second method is commonlyused and appears to be the most flexible but necessitates fresh econo-metric estimates of import elasticities. The third, although structurallyderived from micro-foundations of consumer demand theory, can bemore restrictive, and there is no warranty that these estimates will besuperior for practical applications.

The purpose of this article is to assess these three alternative meth-odologies for computing the elasticity of imports. The models areapplied to data on basic grain markets in El Salvador. The results showthat the derived estimates tend to produce higher elasticity estimatesand that the Armington model performs poorly. The results thus sup-port the use of direct estimation from ad hoc import demand modelswhen time and data allow or the use of derived estimates when thepurpose of analysis is to support practical policy-making decisions.

GENERAL APPROACH

In order to discuss the different elasticity estimates, it is useful tothink of them in the following context. For a given commodity, excess

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Rigoberto A. Lopez 23

demand for (Mi) imports can be represented by

(1)

where i is a commodity index, Pi is the commodity’s price, Yi is con-sumer income, and Zi is a vector of input costs and weather. Di(�)denotes domestic consumer demand and can be derived theoreticallyfrom constrained utility maximization. Si (·) denotes supply by domes-tic producers and can be derived theoretically from either a productionfunction representation of technology or a profit function.

Equation (1) represents the effective import demand function incases where border prices are being transmitted perfectly to domesticprices. There are myriad reasons why this might not be the case,including government policies that insulate domestic markets (Bre-dalh, Meyers, and Collins, 1979; Devadoss and Meyers, 1990). Thisnecessitates accounting for the possibility of imperfect price transmis-sion. Following Bolling (1988), the specification of price transmissionbegins with an identity known as the price linkage equation, whichlinks the domestic price to the border price:

(2)

where Pf is the world price in foreign currency for the commodity inquestion, e is the nominal exchange currency per unit of the relevantforeign currency, and ti is the transfer cost which includes transporta-tion cost and any tariffs. Letting transfer costs remain constant andletting Pi

w = ePf be the world price in domestic currency, the pricetransmission elasticity (�i) can be depicted by

(3)

where 0 � �i � 1 ( = 0 for zero price transmission and = 1 for perfectprice transmission).

THE DATA

Data sources also included International Financial Statistics of theInternational Monetary Fund (Gross Domestic Product and the con-sumer price index), Política Agrícola volumes II (Pleitez, 1992) andIII (Ramos, Worman, and Hugo, 1993) of the Ministerio de Agricultu-

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ra y Ganadería of El Salvador for production, yields, imports, andexports. Annual observations were collected for 1980-97. The effectof weather on yields was measured with a Stallings’ index.1 For whitemaize and red beans, the producer prices are used. For rice, the whole-sale prices are used to measure domestic prices.

The international reference prices for each grain were obtainedfrom several sources, depending on the foreign country that served asbenchmark for the grain in question. For white maize and red beans,the producer prices in Honduras, one of the lowest-cost producers inthe region, are used. The reference prices for white corn and red beanprices came from the FAO website (apps.fao.org) for the 1980-97period and were then extrapolated from 1996-97 with Honduran pricedata reported in the Consejo Nacional de Producción, website(http://www.mercanet.cnp.go.cr).2 Used as a reference price, the U.S.gulf price for rice was as reported in the International FinancialStatistics Yearbook (1997a).3 Finally, the exchange rate was used toconvert reference prices to domestic currency units. Exchange rateswere obtained from International Financial Statistics Yearbook(1999).

ALTERNATIVE RESULTS FOR IMPORT ELASTICITIES

Derived Import Elasticities

When imports are perfect substitutes for crops produced domesti-cally, import elasticities can be calculated from domestic demand andsupply elasticities (Johnson, 1977; Goldstein and Khan, 1985). Ma-nipulating equation (1) and using equation (3), a country’s price elas-ticity of demand for imports in year t can be expressed as

(4)

where �mit is the price elasticity of imports for grain i; �it is the price

elasticity of domestic demand (in absolute value); �it is the priceelasticity of domestic supply, and � it is the price transmission elastic-

ity. The terms Wd

it( = Dti/Mti) and W

sit ( = S it/Mit ) are weights attached

to those elasticities. Following Lopez and Ramos (1998), the quantity

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Rigoberto A. Lopez 25

demanded domestically (Dti) was approximated by apparent domesticconsumption ( = production plus imports minus exports). Exportswere minimal and only occurred in a few years simultaneously withimports.

The estimates of �i and �i for basic grains in El Salvador came fromLopez and Ramos (1998). Their long-run estimates of price elasticitiesof supply (�i) were 0.261 for maize, 0.571 for red beans, and 0.222 forrice. Their estimates for price elasticities of domestic demand (�i)were �0.553 for maize, �0.601 for red beans, and �0.530 for rice.

To quantify the response of internal prices to changes in worldprices, the following equation is estimated from equation (2), lettingtransfer costs remain constant,

(5)

where U is the error term accounting for all other changes in P notaccounted for by Pw. The price transmission equations were estimatedvia Seemingly Unrelated Regressions. The last procedure is particularlyappropriate since the error terms in these equations are likely to becontemporarily correlated due to excluded factors that simultaneouslyaffect these commodity markets. The results are presented in Table 1.Thus, the price transmission elasticities for each grain for each year

were estimated by . For the 1987-97 period, the averageprice transmission elasticities were estimated at 1.01 for maize, 0.846for beans, and 0.962 for rice.

The results for derived import price elasticities, from applyingequation (4), are shown in Table 2. The price elasticities of maizeimports averaged �7.529 in the 1986-97 period. Those for beans andrice averaged �6.538 and �3.165, respectively.

Direct Estimation of Import Elasticities

Price elasticities of imports can also be calculated directly fromimport demand functions. The residual demand for imports in (1),using the price transmission relations in equation (2), can be expressedas

(6)

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Since there is no consistent data on �i (transfer costs), it is assumedto be constant over time. Import demand shifters included the grossdomestic product deflated by the consumer price index, a proxy forconsumer income, weather measured by a Stallings’ index, and adummy variable for years of exceptional exports (a few years before1987). The directly estimated elasticity results came from implement-ing a linear function to obtain time-varying elasticities of grain im-ports with respect to each grain’s world price. The econometric results,obtained from seemingly unrelated regressions, using the SHAZAM8.0 software, are shown in Table 1.

Yearly elasticities were obtained by estimating foreach year, where . The estimated elasticities for the 1987-97period are shown in Table 2. The average import price elasticities formaize, beans, and rice were estimated at �1.820, �1.991, and�0.658, respectively.

TABLE 1. Econometric Results for Basic Grains in El Salvador, 1980-97.

Price Transmissions Maize Beans Rice

World Price 1.093 1.1422 1.226(19.021) (19.333) (13.883)

Intercept �0.434 28.716 5.316(�0.138) (2.779) (0.486)

Import Demands

Deflated Border Price �53.046 � 105 �24.007 � 104 �16.281 � 104

(�3.211) (�2.062) (�3.1613)

Real GDP 34.836 �0.578 2.549(1.254) (�0.114) (0.459)

Weather �37.242 � 105 21.64 � 104 17.834 � 104

(�1.784) (0.776) (0.464)

Dummy for Export �10.141 � 105 �15.868 � 104 �23.088 � 104

Years (�1.839) (�1.345) (�1.609)

Armington Models

ln 2.168 2.404 0.085(2.583) (0.678) (0.091)

Dummy for Export �1.710 �11.448 �1.587Years (�4.907) (�4.217) (2.060)

Note: The parameters were estimated via seemingly unrelated regressions.

Pwi

Pi /( )

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Rigoberto A. Lopez 27

Armington Estimates

The previous two methods do not explicitly address the possibilitythat domestic and imported commodities may not be perfect substi-tutes. This assumption is less severe for white maize and beans thanfor rice, which is mostly imported from relatively far-away places(e.g., the United States and Thailand) where differences betweenhome-grown and foreign varieties may be significant.

To address the issue of imperfect substitution, an Armington modelis adopted since it distinguishes products by place of production. As iscustomary, two types of products are allowed: the home country’s andthat of the rest of the world (the benchmark country that exports thegrains in question to El Salvador).

The Armington model, which has been used extensively, assumestwo stages of budget allocation. The first stage is allocation to productcategories in which each basic grain is a category, and the second isallocation of these expenditures between domestic and foreign grains.

TABLE 2. Alternative Estimates of Price Elasticities of Imports for Basic Grainsin El Salvador, 1987-97.

Derived Estimates Direct Estimates Armington Estimates

Year Maize Beans Rice Maize Beans Rice Maize Beans Rice

87 �16.678 �2.909 �2.909 �4.855 �1.429 �0.576 �2.168 �2.404 �0.085

88 �8.879 �8.913 �7.367 �2.218 �4.536 �2.191 �2.168 �2.404 �0.085

89 �4.869 �3.927 �5.012 �1.247 �1.493 �0.974 �2.168 �2.404 �0.085

90 �14.951 �4.538 �2.393 �4.089 �1.519 �0.427 �2.168 �2.404 �0.085

91 �1.919 �3.401 �2.083 �0.503 �0.865 �0.510 �2.168 �2.404 �0.085

92 �7.359 �6.474 �4.513 �1.432 �0.865 �0.857 �2.168 �2.404 �0.085

93 �7.347 �4.141 �2.793 �1.281 �1.168 �0.397 �2.168 �2.404 �0.085

94 �4.427 �3.434 �2.562 �1.344 �0.765 �0.369 �2.168 �2.404 �0.085

95 �3.608 �2.699 �1.970 0.529 �0.351 �0.329 �2.168 �2.404 �0.085

96 �4.285 �21.617 �1.724 �0.833 �6.365 �0.279 �2.168 �2.404 �0.085

97 �8.492 �9.860 �2.540 �1.688 �2.549 �0.327 �2.168 �2.404 �0.085

Mean �7.529 �6.538 �3.165 �1.820 �1.991 �0.658 �2.168 �2.404 �0.085

St Dev 4.644 5.549 1.754 1.411 1.847 0.553 0 0 0

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The conventional form of the resulting demand function is a constantelasticity of substitution (CES) function that can be expressed as:

(7)

where 1� is the natural log operator and �i is the elasticity of substitu-tion between the domestic and the imported grain i. Note that theimport elasticity of demand is then given by:

(8)

Equation (7) was estimated for white maize, beans, and rice in ElSalvador using 1980-97 data. The results for �

mit , presented in Table 2,

are �2.168 for maize, �2.404 for red beans, and �0.085 for rice.Obviously, the Armington estimates are more in line with the ‘direct’estimates. To assess these differences more formally, the followingsection presents several statistical comparisons of the results from thethree methods presented in this section.

COMPARISON OF RESULTS

To assess differences among the elasticity estimates in Table 2,t-tests were conducted to ascertain whether the means of the importelasticities for a given grain under the three methods were significant-ly different from each other. Of the three resultant tests, Table 3 showsthat one (derived vs. direct estimates for rice) out of nine differencesof means was statistically significant at the 5% level. Two additionaldifferences of means (derived vs. direct estimates for maize and de-rived vs. Armington estimates for rice) were also statistically signifi-cant at the 20% level (critical t-statistic = 1.372 for 10 d.f.). All othermean differences were not statistically significant at this level.

The Spearman-Shearson rank correlation coefficients do show acongruous ranking of the estimated import elasticities for the direct vs.derived elasticity methods. The correlation coefficients are 0.97 formaize, 0.80 for beans, and 0.63 for rice. As for the Armington esti-mates, which are time-invariant, the Spearman-Shearson coefficientswere below 0.5 in all cases when compared to the direct and derivedestimates rankings, except for the correlation between the Armingtonand direct estimates for rice (ρ = 0.80). Thus, in general, both themean and ranking of the estimated import elasticities were fairly con-

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Rigoberto A. Lopez 29

TABLE 3. Means Test Statistics for Alternative Estimates of Price Elasticitiesof Import for Basic Grains in El Salvador, 1987-97.

Estimate

Estimate Type Direct ArmingtonMean Differences (t-statistics)

Maize:

Derived �5.709 �5.361(�1.738) (�1.154)

Direct 0.348(0.247)

Red Beans:

Derived �4.546 �4.134(1.157) (0.745)

Direct 0.413(0.220)

Rice:

Derived 2.507 �3.080(0.332) (�1.756)

Direct �0.573(�1.031)

Note: Only the 1987-97 elasticities are included. The differences of mean should be read as the means of rows minus the means of the columns.

sistent between the direct and derived estimates, whereas the Arming-ton model estimates were outcast for the sample in question.4

CONCLUSIONS

It is clear that the derived estimates tend to produce higher esti-mates of import elasticities (even when price transmission is taken intoaccount) than direct estimations of these elasticities via an ad hocimport demand or an Armington model. On the other hand, there areno benefits from using an Armington model to estimate these elastici-ties. In fact, except for maize, the model fits the data poorly.

Although the results obtained here are dependent upon the specificfeatures of the models selected and the sample data, it is concludedthat the direct estimate of import elasticities of demand with flexibleforms of import demand equations offers the best performance when

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time and data availability are on the researcher’s side. When time anddata are lacking, the derived estimates offer the best hope of a first-approximation response of imports to changing world prices. At thesame time, the derived estimates under various price transmissionassumptions may offer the best guesstimates of the potential importflows once the market in question is liberalized.

NOTES

1. First, expected yields for maize, beans, and rice, were obtained by regressingyield on time and by using the predicted values as expected yield. Then a weathervariable was measured as the ratio of actual to expected yield. The resulting weathervariables were correlated, and the alternative crop whose weather was most highlycorrelated with a given basic grain was chosen in lieu of a grain’s own weather vari-able to avoid spurious correlation.

2. Nicaragua, although an important supplier to El Salvador now, was excludedbecause of years of hyperinflation and hyperdevaluation in the late 1970s and in the1980s. Thus, the price and exchange rate observations were very erratic. Although asignificant amount of white corn is imported from Guatemala (especially from near-border areas), several attempts to weight the Guatemalan exchange rate and pricesgenerally deteriorated the statistical performance of the price transmission equationfor white corn. In addition, Guatemala has had higher internal prices than El Salvador.

3. An important issue arose when deciding what price level to use as the internalprice for rice. There was a huge discrepancy between the domestic producer priceand the wholesale price for rice (average of 79 vs. 131 colones per ton in the 1980-97period for rice in grain), which was atypical of the other grains. It is not clear whythis was the case, but the wholesale price appears to be a more sensible choice, espe-cially when compared with the domestic price which is clearly also a wholesale ex-port price.

4. The results for the Armington model are consistent with those of Ito, Chen, andPeterson (1990), based on their analysis of the world rice market in that the singleconstant elasticity assumption may not be appropriate for analyzing agriculturaltrade. To partially address this problem, a model with time-varying Armington elasti-cities was estimated but did not appear to improve the results. The mean (standarddeviation) import elasticities for the 1987-97 period were �0.59 (0.19) for maize,�6.77 (0.52) for beans, and 0.27 (0.11) for rice.

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Bolling, Christine. (1988). ‘‘Price and Exchange Rate Transmission Revisited: TheLatin American Case.’’ In Elasticities in International Agricultural Trade, ColinA. Carter and Walter C. Gardiner, eds. Boulder, CO: Westview Press.

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Bredahl, E., W.H. Meyers, and K.J. Collins. (1979). ‘‘The Elasticity of ForeignDemand for U.S. Agricultural Products: The Importance of the Price Transmis-sion Elasticity.’’ American Journal of Agricultural Economics, 61(1): 58-63.

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Ito, S., D.T. Chen, and E.W.F. Peterson. (1990). ‘‘Modeling International TradeFlows and Market Share for Agricultural Commodities: A Modified ArmingtonProcedure for Rice.’’ Agricultural Economics, 4(3/4): 315-333.

Johnson, P.R. (1977) ‘‘The Elasticity of Foreign Demand for U.S. Agricultural Prod-ucts.’’ American Journal of Agricultural Economics, 59: 735-736.

Lopez, R.A. and H.H. Ramos. (1998). Supply Response and Demand for BasicGrains in El Salvador. Agribusiness: An International Journal, 14(6): 475-481.

Ministerio de Agricultura y Ganadería of El Salvador, Costos de Producción, vol-umes 1979-80 through 1996-97, Dirección General de Economía Agropecuaria(DGEA), San Salvador, El Salvador.

Pleitez, W. (1992). ‘‘Hacia una Estrategia Integral de Seguridad Alimentaria en ElSalvador.’’ Política Agrícola, Vol. II, Ministry of Agriculture and Livestock, SanSalvador, E.S., February 1992.

Ramos, H.H., F. Worman, and C. Hugo. (1993). ‘‘Estudio de Repuesta de la Produc-ción de Granos Básicos en El Salvador.’’ Política Agrícola, Vol. III, Ministry ofAgriculture and Livestock, San Salvador, E.S., June 1993.

Secretaria del Consejo Agropecuario Centroamericano. (1997) Granos Basicos enCentroamerica: Informacion Estadistica 1990-96. Sistema Centroamericano deInformacion de Granos Basicos, Reunion Tecnica Preparatoria, Montelimar, Nic-aragua, May 1997.

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