**2. Literature Review**

Medication price studies tend to rely on cross sectional data (Daalen et al. 2021). Some studies have documented links between market structures and competitive effect pricing patterns (Barigozzi and Jelovac 2020; Granlund 2022). Potential time series linkages among cross-country industry aggregate prices have not received as much attention. While regulatory and other international boundary barriers may limit the strength of those pricing links, very little empirical evidence regarding that possibility has been previously conducted.

Lower priced medicines are sought by consumers due to budget constraints. As shown by the "generics paradox", there is no guarantee that the availability of lower priced drugs will cause prices to decline (Vandoros and Kanavos 2013). However, cross-sectional price data indicate that United States consumers can save more than USD 1000 annually by purchasing prescription medicines online in Mexico (Fullerton et al. 2014). There is substantial evidence that consistently confirms that brand name pharmaceuticals are substantially more expensive in the United States than in Mexico and most other countries

**Citation:** Fullerton, Thomas M., Jr., and Steven L. Fullerton. 2022. Aggregate Online Brand Name Pharmacy Price Dynamics for the United States and Mexico. *Economies* 10: 112. https://doi.org/10.3390/ economies10050112

Academic Editors: Ralf Fendel, Robert Czudaj and Sajid Anwar

Received: 24 March 2022 Accepted: 10 May 2022 Published: 12 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

(Mulcahy et al. 2021), but no study of how those prices evolve over time or if cross-country movements in those prices are correlated.

Brand name medicines tend to be more expensive in lower- and middle-income countries once income and cost of living differences are taken into account, but not in dollar terms based on currency market exchange rates (Moye-Holz and Vogler 2022). Patients in the United States are able to take advantage of the latter with respect to pharmaceutical products purchased in Mexico either in-person (Fullerton and Miranda 2011) or online (Fullerton et al. 2014). This study examines whether the online prices for medicines sold to customers from both countries are correlated over time.

#### **3. Data and Methodology**

The University of Texas at El Paso Border Region Modeling Project collects prices every month for brand name medicines that can be purchased online in Mexico and the United States. These prices do not include value-added taxes in Mexico, sales taxes in the United States, or shipping and handling costs, nor do they include the cost of doctor appointments. International medicines can be legally imported by individual consumers in the United States as long as the amounts purchased do not exceed 90-day supplies. Furthermore, those purchases can only be for personal use (CBP 2011; Fullerton et al. 2014).

The sample period is from January 2007 through December 2021. Prices for the 50 top selling medicines are for equal dosages on a per unit basis, exclusive of shipping fees, handling charges, and taxes. Websites in both countries advertise their services in English and quote product prices in dollars. The internet sites that sell the medicines do not always offer all 50 brand name products, so multiple sites have to be sampled. Unweighted averages for both sets of prices are calculated from the data collected for each month.

Table 1 reports summary statistics for both average price variables. In line with conventional wisdom, the average price in Mexico is noticeably lower than that of the United States. However, the north-of-the-border price index is somewhat more variable than that observed for Mexico. The standard deviation of the United States online price index is double the magnitude of the southern online price index. While that is impressive, it should be noted that the difference in the magnitudes of the coefficients of variation is much more moderate. The data for both indices are slightly left-skewed, but fairly close to being symmetric. Both sets of price data are notably platykurtic.


**Table 1.** Summary Statistics.

Notes: Sample Period: January 2007—December 2021. Unit of Measure: United States Dollars. AVG\_\$\_MX— Average Brand Name Medicines Price in Dollars for Mexico Internet Sites. AVG\_\$\_USA—Average Brand Name Medicines Price in Dollars for USA Internet Sites. Std. Dev.—Standard Deviation. CV—Coefficient of Variation. Data Web Sites—goodrx.com accessed on 15 December 2021, healthwarehouse.com accessed on 15 December 2021, medicinesmexico.com accessed on 15 January 2020, medsmex.com accessed on 15 December 2018, mexmedsforyou. com accessed on 15 December 2021.

A linear transfer function autoregressive moving average (LTF ARIMA) methodology is employed to examine the dynamic relation between the two indices. For monthly time series data, the LTF ARIMA approach has proven useful in other contexts involving international economic data for the United States and Mexico (Fullerton and Solis 2020). Due to the magnitude of the United States market for pharmaceutical products, causality between the two price indices is expected to run north-to-south. If that were not the case, then an alternative method such as vector autoregression would be required (Diebold 2007).
