Artículos

 

Milkshake Prices, International Reserves, and the Mexican Peso

 

Thomas M. Fullerton, Jr.* David Torres**

 

* Professor-researcher, University of Texas at El Paso. E-mail: tomf@utep.edu.

** Economist, Finance Department, El Paso Water Utilities. E-mail: dtorres@epwu.org.

 

Fecha de recepción: 27 de septiembre de 2004.
Fecha de aceptación: 24 de noviembre de 2004.

 

Abstract

Menu prices from 13 international restaurant franchises that operate m both El Paso and Ciudad Juárez are utilized to examine the behavior over time of the peso/dollar exchange rate. Parametric and nonparametric tests indicate that the price ratio alone provides a biased estimator for the exchange rate. In addition to the multiproduct price ratio, the empirical analysis also incorporates interest rate parity and balance of payments variables. The combination of unique microeconomic sample data with national macroeconomic variables illustrates one manner in which border economies provide information regarding the interplay of financial markets between Mexico and the United States.

Keywords: price parity, exchange rates, Mexico, United States, border economics.

 

Resumen

A partir de los precios del menú de restaurantes de 13 franquicias internacionales que operan en El Paso y Ciudad Juárez se examina el comportamiento del tipo de cambio del peso. Pruebas paramétricas y no paramétricas indican que la relación de precios representa una medida sesgada para el tipo de cambio en términos estrictamente aritméticos. Además de la relación de precios de productos múltiples, el análisis empírico también incorpora tasas de interés de los dos países y una variable que refleja cambios en la balanza de pagos en México. La combinación de datos microeconómicos con datos macroeconómicos ilustra una de las maneras en que las economías fronterizas aportan información acerca de los nexos financieros entre México y Estados Unidos.

Palabras clave: paridad cambiaria, tipo de cambio, México, Estados Unidos, economías fronterizas.

 

INTRODUCTION¹

Exchange rate studies that analyze geographic and commodity group data have become relatively common in recent years (Engel and Rogers, 1996, 2001). This is, in part, due to the popularity of analyzing "hamburger" currency indexes, which are based on widely consumed menu items served at popular franchise restaurants (Ong, 1997; Anonymous, 2002). It is also because this approach utilizes microeconomic data that were previously unavailable and that complement the traditional macroeconomic data sets that rely on aggregate price variables (Pakko and Pollard, 1996; Evans and Lyons, 2002).

This article utilizes cross-border menu price data for milkshakes, pizzas, steaks, and other items to examine the exchange rate behavior of the Mexican peso. The analysis takes advantage of a multicomponent price data set for international restaurants, which matches menu items found in the sister cities of El Paso, Texas, in the United States and Ciudad Juárez, Chihuahua, in Mexico. On its own, the cross-border restaurant price index has been found to provide a biased estimate of the exchange rate between the peso and the dollar (Fullerton and Coronado, 2001). Accordingly, the modeling strategy employed here goes beyond that implied by purchasing power parity (Balassa, 1964) to include elements suggested by interest rate parity and balance of payments hypotheses (Aliber, 1973; Blanco and Garber, 1986; Throop, 1993; Zhou and Mahdavi, 1996).

We begin with a brief overview of related exchange rate studies, which focus primarily on variants of purchasing power parity (PPP) and interest rate parity (IRP) models. These PPP studies include recent investigations of international food-price ratio comparisons to exchange rates. We then turn to a description of our data collection efforts and the theoretical models utilized to analyze the data. A geographically unique price ratio, based on a sample of approximately 70 menu prices collected monthly, is utilized as the PPP component. Interest rate information is calculated using 91-day Certificados de la Tesorería de la Federación (Cetes) in Mexico and 90-day Treasury Bills (T-Bill) in the United States. Balance of payments information is introduced by employing a ratio of international reserves to imports in Mexico. The article concludes with a summation of the empirical results and suggestions for future research.

 

LITERATURE REVIEW

In an era of variable, and occasionally volatile, exchange rates, their monitoring has come to occupy a central role in both corporate planning and public policy analysis. Efforts to reduce foreign exchange rate risk have increased the interest in studies addressing the determination of exchange rates. A large percentage of these studies rely upon PPP and IRP modeling frameworks (Marston, 1997). Short-run departures from PPP are fairly common, but a variety of studies report long-run evidence that favors different versions of this hypothesis (Jorion and Sweeney, 1996; Wu and Wu, 2001). Given its regional history of periodic financial instability, efforts to model Latin American exchange rates frequently rely on balance of payments information to augment the more widely used PPP and IRP frameworks (Blanco and Garber, 1986; Fullerton, Hattori, and Calderón, 2001).

Several well-known techniques are based on PPP frameworks. One common approach is to calculate trade-weighted real exchange rate indexes. Under that method, an index number greater than 100 indicates overvaluation and an index number below 100 points to currency undervaluation (Fuentes, 2002). A second popular technique deals with implied nominal exchange rate calculations based upon national price index movements relative to a specific base period (Cheung and Wong, 2000; Lara y Beltrán del Río, 2002). A third approach was introduced more than a decade ago by The Economist magazine: "Burgernomics" takes advantage of the existence of an international franchise restaurant menu to develop a simplified PPP index (Ong, 1997). The strategy relies on using the globally popular hamburger, a signature menu item produced in 120 countries, as the homogeneous comparison good. Although not intended to replace careful currency market analysis or more technically sophisticated monitoring devices, the burger index correctly signaled that the Euro would decline relative to the U.S. dollar following the introduction of the new currency in 1999 (Anonymous, 2002).

The popularity of the easy to understand burger index served as a catalyst for additional empirical efforts that make more extensive use of restaurant pricing patterns within the PPP framework. Michael Pakko and Patricia Pollard (1996), examining the reliability of PPP and burger indexes for 15 currencies relative to the U.S. dollar, found that the conditions for absolute PPP, under which ratios of national price indexes approximate exchange rates, do not hold in the short run. The relative version of PPP, which states that percent changes in the prices levels will lead to similar proportional changes for exchange rates, also does not hold in the short run. Potential explanations for those outcomes include barriers to trade, especially in agricultural products, causing prices of goods to differ across borders; variations in non-tradable-goods prices such as real estate and utilities, leading to generalized price differences among countries; oligopoly market structures contributing to further price misalignments between regions; current account imbalances; and productivity gaps, which also contribute to international price divergences. Those factors notwithstanding, Ong (1997) obtains results that indicate that a burger-based PPP index does hold in the long run.

Other authors have utilized larger baskets of goods and consumer price sub-indexes to examine evidence implied by a cross section of products (Fraser, Taylor, and Webster, 1991; Engel and Rogers, 1996, 2001; Jenkins, 1997). This branch of the literature highlights several factors that can cause pricing patterns to deviate across markets. In particular, distances and transportation costs are generally found to contribute directly to the magnitudes of price differences between regions (Chen and Finney, 2002). Those deviations are also found to be greater in cases where international borders also serve to intensify market-segmentation effects normally observed for metropolitan markets separated by distance. Differences in regional business cycles and industrial composition have also been identified as sources of temporary divergences between price patterns and exchange rates (Clark, Sawyer, and Sprinkle, 1997, 1999, 2001).

Additional factors can also affect price ratio comparisons between markets at different stages of development. Several studies (Balassa, 1964; Summers and Heston, 1991; Heston and Summers, 1996) argue that exchange rate conversions will overstate income estimates for higher income countries, such as the United States, and understate them for lower income nations, such as Mexico. Vikas Kakkar (2001) reports evidence that non-tradable price differentials play an important role in PPP deviations observed for the peso/dollar exchange rate. Also contributing to those numeric gaps are differing capital-labor ratios, menu costs, and taxes (Bhagwati, 1984; Rogers and Jenkins, 1995). As pointed out by Dornbusch (1976), currency market overshooting can also result from interest rate disparities combined with asset-market and goods-market adjustment differences. Given the above, it would not be surprising for price ratios for country pairs to differ from exchange rates.

Much of the evidence reported by Thomas Fullerton and Roberto Coronado (2001) corroborates the potential divergence between currency quotes and restaurant price ratios for Mexico and the United States. That study examined menu prices between franchise restaurants in El Paso, Texas, and Ciudad Juárez, Mexico. They sample priced for more than 72 menu items offered at 13 franchise restaurants found on both sides of the border.² In nearly two-thirds of the monthly observations, menu prices on the south side of the border were lower than would be anticipated based on a comparison to the peso/dollar exchange rate and the counterpart menu items in the United States. The restaurant price ratio was correlated with the exchange rate, but it provided a biased predictor for it. In that study, menu prices on both sides of the border changed frequently but in a manner apparently unrelated to variations in peso/ dollar quotes. Some portion of the deviation between the price ratio and the exchange rate may have also resulted from the local-currency pricing effect, identified for Mexico by Charles Engel (2001).

Of course, PPP models represent only one approach to the analysis of currency markets. Many studies have reported at least partial evidence in favor of IRP modeling frameworks (Aliber, 1973; Gregory, 1987; Marston, 1997). With respect to the Mexican peso, Hoe E. Khor and Liliana Rojas-Suarez (1991) reported empirical results that support the uncovered IRP hypothesis. That study also highlighted difficulties that the Mexican government will likely face if it attempts to lower interest rates before attaining overall economic stability. Historically, financial disequilibria have played prominent roles in currency market volatility affecting the peso (Gil-Díaz and Carstens, 1996).

Several authors have examined factors that can cause developing country exchange rates to depreciate rapidly. Those studies generally incorporate aspects of both PPP and IRP modeling strategies. A frequent approach employed for Latin American currencies includes balance of payments variables in the various model specifications (Blanco and Garber, 1986; Fullerton, Hattori, and Calderón, 2001). This article relies on a similar framework that utilizes a more extensive sample of the Fullerton and Coronado (2001) restaurant price ratio as the PPP component in the empirical analysis.

 

DATA AND METHODOLOGY

An elementary representation of one model that predicts movements in the peso by utilizing purchasing-power and interest-rate components is:

where NEX_t is the nominal exchange rate between the peso and dollar in month t, PR is the price ratio between restaurant products in Mexico and the United States in month t, and IR_f is the interest rate ratio between Mexico and the United States for the same period. Variants of this basic formula have been employed in several earlier studies (Zhou and Mahdavi, 1996; Marston, 1997; Fullerton and Coronado, 2001).

The purchasing power parity component is calculated using the monthly ratio of menu prices from Ciudad Juárez and El Paso. The sample is based on menu price data obtained from a variety of cross-border franchise operations, including four hamburger chains, three pizza franchises, two fried chicken restaurants, two Mexican food establishments, one sandwich chain, and one upscale family restaurant. Two of the 13 companies are headquartered in Mexico; the rest are based in the United States. Data were collected by visiting the franchise pairs during the third week of each month from July 1997 through June 2001.

The comparison items are largely homogeneous. Because they are designed to be eaten quickly, these food items are not tradable goods in the classical sense. Indeed, it is illegal to bring pork products, fresh fruit, and fresh vegetables, which are used in many of the products included in the monthly sample, into the United States. Although the menu items are not tradable commodities, arbitrage opportunities exist in Ciudad Juárez because prices there are quoted in pesos, but payments are accepted in either currency. Separate evidence reported for Mexico, using national data series, indicates that deviations between the exchange rate and the price ratio are likely due to non-tradability (Kakkar, 2001). For the multiproduct restaurant price ratio discussed here, arbitrage pressures potentially serve to minimize the magnitudes and durations of any price inequalities that result from currency market shocks (Asplund and Friberg, 2001).

Using the raw data collected on both sides of the border, individual price ratios are then calculated by dividing the price in pesos by the price in dollars for each menu item. Statistical moments are also calculated for all of the monthly samples. The first means and variances are used to conduct t-tests for sample mean and exchange rate equality. Recent PPP studies (Fullerton and Coronado, 2001; Wu and Wu, 2001) indicate that the monthly data utilized in these samples may not follow a normal distribution. Given that, the third and fourth moments, skewness and kurtosis, are used to conduct chi-square tests for sample distribution normality (Bera and Jarque, 1981). When non-normal sample data are encountered, a nonparametric test is used to test for sample mean and exchange rate equality. The procedure, a Wilcoxon signed-rank test, is distribution free (Daniel, 1978). In cases where the exchange rate and price ratio series are equal, the β₂ regression coefficient estimated for the interest rate ratio in Equation (1) will likely be statistically indistinguishable from zero.

The interest rate variable shown in Equation (1) is the ratio of the yields for the 91-day Cetes to the 90-day T-Bill. (For Mexican interest rate data, see the Banco de México web site [www.banxico.org.mx]; for the U.S. interest rate data, see the Federal Reserve Bank of St. Louis website [www.stlouisfed.org].)

Balance of payments pressures occasionally play a role in Latin American currency markets (Blanco and Garber, 1986). To take that possibility into account, an import coverage ratio is introduced, which changes the basic model specification to:

In Equation (2) the import coverage ratio variable is calculated as the ratio of monthly international reserves in Mexico, net of gold deposits, to monthly imports of goods and services measured in U.S. dollars. (Data are available at www.banxico.org.mx or from the International Monetary Fund [2002].) The exchange rate is hypothesized to vary inversely with respect to the import coverage ratio variable, implying that β₃ will be less than zero.

 

EMPIRICAL RESULTS

Parametric and nonparametric statistical tests are conducted for equality between the average monthly price ratios and exchange rates. For the parametric approach, a standard t-test is conducted for equality between the arithmetic means of the price ratios and the average nominal exchange rate for every month of the sample. The 48-month sample included four episodes of relatively rapid nominal depreciation, during which the peso declined by 4% or more in a single month (November 1997, October 1998, May 1999, and June 2000). The peso also appreciated notably relative to the dollar in March 1999, July 2000, and April 2001 (table 1).

In 26 of the 48 months in the sample, the price ratio differed significantly from the corresponding exchange rate (table 2). In those 26 months, the price ratio always fell below the exchange rates. This implies that menu prices in Mexico are less expensive than counterpart prices in the United States, which may reflect labor-cost differentials and other variables, such as own-price and cross-price elasticities of demand between the two economies (Heston and Summers, 1996). In 22 of the 30 periods from January 1999 to June 2001, the price ratio did not differ significantly from the exchange rates. Although the apparent convergence of the two series is fairly impressive, the t-test employed assumes data normality. In order to examine whether the monthly bi-national restaurant data meet this requirement, a chi-square test is utilized (Bera and Jarque, 1981; Pindyck and Rubinfield, 1998).

The results of the chi-square test for normality of the monthly price data (table 3). In all but seven months, the null hypothesis of the price ratio normality is rejected at the 5% significance level. Consequently, a Wilcoxon signed-rank nonparametric test is introduced to minimize the risk of incorrect inference associated with the t-test results. The latter procedure is a distribution-free test and does not require assumptions regarding the density function of the variable examined (Daniel, 1978).

Results for the Wilcoxon signed-ranks test show that at the 5% significance level, the null hypothesis of mean price ratio equality with the average nominal exchange rate is rejected in 35 of the 48 months (table 4). As in the case of the t-test results (table 2), the Wilcoxon signed-ranks tests fail to reject the null hypothesis only for periods in 1999, 2000, and 2001. That may imply that the initial evidence (Fullerton and Coronado, 2001) of exchange rate deviations from the price ratio PPP measure represent only temporary departures from the norm for the cross-border restaurant markets. If the two series are statistically equal to each other, it raises a question regarding shock dissipation or speed of realignment when currency shocks occur.

As numerous authors have pointed out (Zhou and Mahdavi, 1996; Marston, 1997), such temporary deviations from PPP may result from interest rate differentials between trading partners such as Mexico and the United States. Deviations from PPP may also result from balance of payments fluctuations (Blanco and Garber, 1986). Regression output, generated for an exchange rate equation that includes contemporaneous lags of the PPP restaurant price ratio, interest rate differential, and import coverage ratio variables, indicates that the coefficients for each of the regressors are statistically significant, but the coefficient for the interest rate ratio is greater than zero (table 5). This implies that if interest rates in Mexico rise relative to those in the United States, the peso will depreciate. That result runs counter to the hypothesized sign for β₂ discussed above. The equation in table 5 also includes a statistically significant autoregressive parameter at lag 1 to correct for serial correlation.

To confirm the results in table 5, 26 separate versions of Equation (2) involving up to four lags of the explanatory variables were also estimated. In 25 out of 26 regressions, the coefficient for the interest rate ratio was both positive and significant. Although counterintuitive, those outcomes confirm a positive relationship between the interest rate ratio and the exchange rate during the sample period studied. Several scholars have suggested that such a result may reflect monetary circumstances in Mexico in which upward interest rate movement reflects the inflationary consequences of peso depreciations. That possibility may warrant investigation once additional sample data become available (for additional similar arguments, see Banco de México, 1998).

Given the apparently robust results associated with table 5, several observations can be made with respect to the behavior of the currency market in Mexico. One is that the fairly strong linkage between the restaurant price ratio and the exchange rate reported by Fullerton and Coronado (2001) is confirmed. A second observation is that balance of payments shocks and other market developments contribute to periodic deviations from PPP-implied values of the peso. Perhaps unsurprisingly, the information reported in table 5 indicates that successful monitoring of the exchange rate in Mexico will involve a combination of PPP and other international financial measures. The cross-border restaurant price ratio seemingly offers one means by which this objective may be partially achieved.

The evidence indicates that the cross-border restaurant price index may help in predicting variations in the peso/dollar exchange rate. This may seem surprising given that it does not involve traded goods (Xu, 2003). It is important to remember, however, that arbitrage opportunities exist for border-region restaurant customers since both currencies can often be utilized for payment (Asplund and Friberg, 2001; Yoskowitz and Pisani, 2002). Because the data reported on in this article are exclusive to the border region, it would be helpful to assemble similar information for other points along the Mexico-U.S. border. Those efforts would allow panel estimates to be employed to examine deviations from parity and adjustment speeds to shocks (Fleissig and Strauss, 2000).

 

CONCLUSION

A variety of research efforts in recent years have utilized multinational franchise restaurant price comparisons with the objective of better understanding international currency valuations. Mixed evidence has been reported with respect to the outcomes from testing various versions of the purchasing power parity hypotheses. This article extends one of those earlier efforts, which had indicated that a basket of cross-border menu prices provides a biased estimator for the peso/dollar exchange rate between Mexico and the United States.

In addition to taking advantage of a larger, 48-month sample, the analysis also incorporates currency modeling strategies involving variables designed to reflect interest rate differentials between the two economies and balance of payments shocks that periodically affect Mexico. Estimation results confirm statistically significant relationships between the peso/dollar exchange rate and each of the three explanatory variables. However, the sign for the interest rate differential variable is the opposite of what was hypothesized. The signs for the restaurant price ratio and import coverage ratio parameters are as hypothesized. The estimation outcomes indicate that a strict interpretation of the PPP model is not supported for this short-run data. Nominal price differentials, as measured by the sample of Mexico-U.S. cross-border franchise menu items, do play important roles in monthly exchange-rate variations.

Additional sampling will eventually allow for conducting a more complete set of tests. At present, the sample is not large enough to take advantage of a variety of time series techniques, such as error correction specifications, which would permit disentangling both short- and long-term factors that potentially affect this currency market. New sampling will also make possible testing with respect to the length of time required for price deviations to dissipate following movements in the peso/dollar exchange rate. Additional tests could also be performed if similar data are collected for other cities along the Mexico-U.S. border.

 

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Notes

¹ The authors would like to acknowledge El Paso Electric Company, City of El Paso Office of Economic Development, Wells Fargo Bank of El Paso, National Science Foundation (Grant SES-0332001), and Southwest Center for Environmental Research and Policy (Grant W-04-03) for their support of this research. Tim Roth, Santiago Ibarreche, Richard Sprinkle, Víctor Espinoza, Roberto Tinajero, and two anonymous referees provided helpful comments. Armando Aguilar and Brian Kelley provided econometric research assistance.

² The number of restaurants in the sample varied somewhat in response to menu changes in either or both cities and locale closures and openings.