This study analyzes the production concept of the Value-Added (VA) chain by applying an alternative framework, as this concept is the main driver of the VA embodied in the intermediate export. VA supply chain spillover (upstream and downstream) of the production activities is investigated. The focal point of this study is to extend Global Value Chains (GVC) based on the multilevel and bilateral trade flow. In brief, there are two main contributions of this paper; the first begins with the originality of this work’s theory which reveals the intermediate input journey among sector-country pairs, and the second is to introduce the optimal GVC participation with the knowledge spillover effect regarding vertical (upstream and downstream) integration. In other words, this paper found that different forms of the VA with traveled products (among countries) provide more precise (sectoral/regional) integration and optimal estimation method. This paper relies on constructed Global Trade Analysis Project Multi-Region Input-Output (GTAP-MRIO) and patent panel datasets. As a result of the analysis, if the product crosses the border only twice as the product returns home to its origin country, the export/import coefficient of the sectoral linkages, which boosts VA and then causes double-counting, is about 1.54 % in terms of (single) country-level data. More importantly, with regard to its contributions with the knowledge spillover effect, traveling products among countries as twice or infinity is to contribute by 1.6% or 154%. Lastly, its contribution to VA presents 0.8% to 72%.