**4. Empirical Results**

A series of F-tests at various lags indicate weak north-to-south unidirectional causality. Given all of the regulatory barriers separating the two markets, that is not surprising. The data indicate that changes in United States brand name online drug prices are accompanied by similar changes in Mexico internet prices, but not vice versa. That implies that medicine prices in Mexico are responsive to price fluctuations in the higher income market.

A cross-correlation function is used to determine the potential lag structure governing the linkages between the two series, (Diebold 2007). The outcome indicates that the reaction of online prices in Mexico is contemporaneous with no subsequent, statistically reliable lagged responses. Parameter estimation outcomes are summarized in Table 2.


**Table 2.** Generalized Least Squares Estimation Results.

The constant term in Table 2 indicates that Mexico online medicine prices tend to lose ground at a rate of roughly USD 0.02 per month. The standard error for that coefficient is fairly large, so the reliability of that estimate is not very strong. Most of the sample period corresponds to a period of relative currency market weakness for the peso, especially after 2015. That may account for some of the steady erosion of the south-of-the-border prices that occur in Table 2.

The slope coefficient indicates that every USD 1 increase (decrease) in United States online prices is accompanied by a USD 0.46 increase (decrease) in Mexico online prices for brand name pharmaceuticals. In the sample means, the magnitude of the coefficient indicates that the elasticity of online prices in Mexico with respect to those of the United States is 0.770. That estimate implies a fairly high degree of cross-border price sensitivity for brand name medicines sold online in Mexico. The computed t-statistic for this parameter estimate is 9.362 with a 0.000 *p*-value.

The overall diagnostics in Table 2 are relatively favorable. The pseudo coefficient of determination is 0.995. Given that, it is not surprising that the computed F-statistic of 42.873 has a *p*-value of 0.000. The specification does not, however, account for all systematic variation in the dependent variable. Residual serial correlation necessitates the inclusion of moving average term at lag 4. That coefficient has a somewhat large standard error, but higher log-likelihood statistic results for the equation when it is included.

As a robustness check, the sample period was shortened by seven years to cover only January 2007 through December 2014. That period is selected because it pre-dates the 2016 US presidential campaign that began in 2015, wherein several major candidates criticized trade with Mexico. Those results also indicate that the internet pharmacy prices charged in Mexico react very quickly to any north-of-the-border price variations and the slope coefficient is almost identical to that reported in Table 2. The coefficients of determination for the shorter period are larger than those reported in Table 2, potentially due to a less friendly trade environment between the two countries and due to the advent of the global pandemic in 2020 (Komkova 2019; Ceylan et al. 2020).

### **5. Conclusions**

Empirical research on global pharmaceutical prices has uncovered numerous interesting commonalities and differences across international markets. This study examines dynamic aggregate price movements for brand name medicines sold over the internet in the United States and Mexico. Although brand name medicine distribution is tightly regulated in both countries, it is legal for consumers to import limited quantities for personal usage.

Over the course of the 15-year sample period, internet medicine prices in Mexico are, on average, 40 percent below the online prices charged in the United States. The prices in Mexico react very quickly to any variation in the prices in the higher-income market. Every USD 1 change in the United States average price index is matched by a USD 0.46 change in the Mexico average price index.

Based on the results reported in this exploratory effort, it seems clear that more research on this topic is warranted. This study employs simple average price measures for both economies. A logical next step would be to examine dynamic patterns among prices for these brand name medicines within a panel setting. The outcomes noted above indicate that cross-border linkages between individual online brand name pharmaceutical prices may be fairly strong.

**Author Contributions:** Conceptualization, T.M.F.J. and S.L.F.; Methodology, T.M.F.J.; Validation, T.M.F.J. and S.L.F.; Formal analysis, T.M.F.J. and S.L.F.; Investigation, T.M.F.J. and S.L.F.; Data curation, S.L.F.; Writing—original draft preparation, T.M.F.J. and S.L.F.; Writing—review and editing, T.M.F.J. and S.L.F.; Supervision, T.M.F.J. and S.L.F.; Project administration, T.M.F.J.; Funding acquisition, T.M.F.J. and S.L.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by El Paso Water, National Science Foundation Grant DRL-1740695, Texas Department of Transportation ICC 24-0XXIA001, TFCU, UTEP Institutional Advancement, and the UTEP Center for the Study of Western Hemispheric Trade.

**Institutional Review Board Statement:** Ethical review and approval are not required for this study due to the fact that anonymous data are used that are not traceable to individuals at any time.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data employed for this study are available upon request from tomf@utep.edu and slfullerton@utep.edu.

**Acknowledgments:** Helpful comments and suggestions were provided by Dan Pastor and two anonymous referees.

**Conflicts of Interest:** The authors declare no conflict of interest.

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