Abstract
Motivated by increasing trade and fragmentation of production across countries, accompanied by income convergence by many emerging economies, we build a dynamic two-country model featuring sequential, multi-stage production and capital accumulation. As trade costs decline over time, global-value-chain (GVC) trade expands across countries, particularly more in the faster-growing country, consistent with the empirical pattern. Via Heckscher–Ohlin forces, GVC trade can generate back-and-forth feedback between comparative advantage and capital accumulation (growth). Moreover, GVC trade increases both steady-state and dynamic gains from trade.
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Notes
We employ a similar method as in Ravikumar et al. (2019) to compute the transitional dynamics in the open economy.
For instance, with two countries and three stages, the set of 8 possible chains is given by \({\mathcal {C}}=\) \(\{(1,1,1);\) (1, 1, 2); (1, 2, 1); (1, 2, 2) (2, 1, 1); (2, 1, 2); (2, 2, 1); \((2,2,2)\}\). Another example is three countries and two stages, and then, the set consists of 9 chains: \({\mathcal {C}}=\{(1,1); (1,2); (1,3); (2,1); (2,2); (2,3); (3,1); (3,2); (3,3)\}\).
The assumption of a unit location is without loss of generality, because country-stage-time efficiency differences that are common to all varieties are captured by \(A^s_{\ell ^s,t}\). In our framework, for a given country in a given time period, \(\prod _{s=1}^{S}\left[ a_{\ell }(v)\left( A^s_{\ell ^s}\right) ^{\gamma ^{s}}\right] ^{{\widetilde{\gamma }}^{s}}\) corresponds to \(\prod _{n=1}^{N}(a_{l(n)}^{n}(z))^{-\alpha _{n}\beta _{n}}\) in Antràs and de Gortari (2020). Antràs and de Gortari (2020) show that the lead-firm approach is isomorphic to an alternative framework with stand-alone producers of different stages making cost-minimizing sourcing decisions for their input in a decentralized manner, with additional assumptions on information available to producers at each stage about the exact costs of producers at earlier stages. We describe our model using only the lead-firm approach.
The usual restriction requires that \((1-\eta )/\theta >-1\), beyond which \(\eta\) plays no substantial role.
Cuñat and Maffezzoli (2007) study trade liberalization in which countries start out with permanent differences in TFP and initially different capital–labor ratios. In this scenario, countries diverge in their investment path, as the country with the higher initial capital–labor ratio accumulates capital, while the other country decumulates capital.
\(1-\text {DCE}_{n,t}\) is a generalization of the “VS” measure from Hummels et al. (2001).
More precisely, there exists a mapping from a multi-sector version of our model to an input–output table. However, as discussed and proved in de Gortari (2019), there is no unique mapping from an input–output table to a GVC model with more than two stages of production.
For the no-GVC case, the DCE is of course equal to one, and thus omitted from the figure.
As mentioned above, the Johnson and Noguera (2012) measure of VAX is similar to our measure of DCE.
Caselli et al. (2020) study the effects of increased openness and exposure to global shocks and find that international trade, through its diversification channel, can lead to lower income volatility.
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Acknowledgements
We thank the guest editor and referees for excellent comments and Robert Johnson for sharing his data on value-added exports. We also thank participants at the Virtual ITM seminar, World Bank, Malaysia, Yale Cowles Foundation Trade Conference, and the SAET conference for their comments. The views expressed here are those of the authors and do not necessarily reflect those of the Federal Reserve Banks of Chicago, Dallas, or the Federal Reserve System.
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