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Third Quarter 2023, 
Vol. 105, No. 3
Posted 2023-07-14

TFP, Capital Deepening, and Gains from Trade

by B. Ravikumar, Ana Maria Santacreu, and Michael J. Sposi


Using a dynamic, multicountry model with capital accumulation, we compute the exact transition paths for 93 countries following a permanent, uniform, unanticipated trade liberalization and calculate the resulting welfare gains from trade. We find that while the dynamic gains are different across countries, consumption transition paths look similar except for scale. In addition,  dynamic gains accrue gradually and are about 60 percent of steady-state gains for every country. Finally, the contribution of capital accumulation to dynamic gains is four times that of total factor productivity.

B. Ravikumar is a senior vice president and the deputy director of research, and Ana Maria Santacreu is a research officer and economist at the Federal Reserve Bank of St. Louis. Michael Sposi is an assistant professor of economics at Southern Methodist University. The authors thank Iris Arbogast for excellent research assistance.


Recently, there have been a few papers computing gains from trade in dynamic models, e.g., Anderson, Larch, and Yotov (2020), Brooks and Pujols (2018), Alvarez (2017), Ravikumar, Santacreu, and Sposi (2019), Mix (2020), and Alessandria, Choi, and Ruhl (2021). In this article, we decompose the dynamic gains from trade into gains from capital accumulation versus gains due to total factor productivity (TFP) changes. 

Comparative advantage dictates that trade liberalization results in allocations that increase measured TFP. The increase in TFP, in turn, increases the rate of return to capital and hence the investment rate in a dynamic model. Under the assumption that the production of investment goods is more tradables intensive than the production of consumption goods, trade liberalization reduces the price of investment relative to the price of consumption; this also increases the investment rate. Thus, trade liberalization yields a higher stock of capital, higher output, and higher consumption.

Our trade environment is the multicountry model of Eaton and Kortum (2002), and our capital accumulation environment is a two-sector neoclassical growth model. We combine the two models, similar to Alvarez (2017) and Ravikumar, Santacreu, and Sposi (2019) (henceforth RSS), and study the interaction between international trade and capital accumulation. A continuum of tradable intermediate goods is used to produce investment goods, final consumption goods, and intermediate goods. A key assumption in our model is that the intensity of tradables is higher in the production of investment goods than in the production of consumption goods. Trade is balanced in each period. Each country is endowed with an initial stock of capital, and capital is accumulated in the same manner as in the neoclassical growth model.  

We calibrate the steady state of the model to reproduce the observed bilateral trade flows across 93 countries. We then conduct a counterfactual exercise in which there is an unanticipated, uniform, and permanent reduction in trade frictions for all countries. We compute the exact levels of endogenous variables along the transition path from the calibrated steady state to the counterfactual steady state and calculate the welfare gains using a consumption-equivalent measure as in Lucas (1987).

We find that the consumption transition paths look similar across countries except for scale and comparing only steady states overstates the gains from trade; the dynamic gains accrue gradually and are about 60 percent of  steady-state gains for every country. We also find that both the dynamic gains and the steady-state gains differ across countries: The dynamic gain for Belize is five times that of the United States, and the contribution of capital accumulation to dynamic gains is four times that of TFP. 

In a closely related paper, Anderson, Larch, and Yotov (2015) also compute dynamic gains from trade. In their model, the transition path is a solution to a sequence of static problems since changes in trade frictions have no effect on the investment rate and the relative price of investment. In our model, the changes in trade frictions affect the transition dynamics of the investment rate and the relative price of investment. 

Read the full article.