Unequal Welfare Gains From Trade Across Countries: The Role of Aggregation and Income Elasticities

Abstract

Sectoral heterogeneity has been shown to affect country-level welfare gains from trade (measured by costs of autarky) that can be calculated by sector-specific trade elasticities and home expenditure shares. However, empirical analyses of multi-sector models are restricted to a limited number of countries and sectors, mostly due to the lack of data on sector-specific home expenditure shares. This paper first proposes a solution to this limitation by changing the way that foreign products are aggregated at the destination country, where ‘unbiased’ multi-sector welfare gains can be captured by using country-specific trade elasticity measures. Second, the restrictive assumption of unitary importer-income elasticity is relaxed, and it is shown that the trade elasticity in the calculation of welfare gains is replaced by the newly-introduced welfare elasticity, a function of trade and income elasticities. Empirical evidence suggests that equal percentage changes in home expenditure shares result in unequal gains across countries depending on their elasticity measures.

Keywords:

• Welfare gains
• income elasticity
• trade elasticity
• welfare elasticity

JEL Classifications:

• F12
• F13
• F14

Acknowledgments

The author would like to thank Sunghyun Henry Kim, Jaebin Ahn and an anonymous referee as well as the participants of presentations at Federal Reserve Bank of Philadelphia, Indiana University, Florida International University, Midwest International Economics Meetings at Drexel University, Midwest Macroeconomic Meetings at Vanderbilt University, and Southern Economic  Association Annual Meetings at Fort Lauderdale, FL for their helpful comments and suggestions. The usual disclaimer applies.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Notes

1 The derivation of such an expression is shown in the Appendix for a representative model of the literature in a multi-sector framework.

2 For example, sector shares and sector-specific home expenditure shares are calculated by using the World Input–Output Database for 34 countries in Costinot and Rodríguez-Clare (2014), while they are calculated by using the Global Trade Analysis Project for 50 countries in Ossa (2015). However, as shown by Timmer et al. (2015), these input–output tables have several weaknesses such as issues due to merging production and trade data, inconsistency across countries and over time, or the assumption of technology homogeneity across firms. As discussed in details below, this paper deviates from these problems by considering an alternative method of aggregation for individual consumption goods.

3 Another reason for this limitation is to utilize input–output tables to capture intermediate-input trade or the non-traded sector. Nevertheless, as shown by Ossa (2015) and Giri et al. (2021) in different contexts, increased disaggregation and heterogeneity obtained from these input–output tables do not necessarily lead to higher or lower gains from trade calculations when model-consistent elasticity estimates are employed.

4 We show empirical evidence for this claim in the Appendix, where we show that restricting the sample to a certain number of countries (using the country list in the World Input–Output Database) results in much lower trade elasticity estimates compared to using the complete list of countries in the UN Comtrade database.

5 Among many others, studies such as by Arkolakis et al. (2012), Caliendo and Parro (2015), Ossa (2015), Imbs and Mejean (2015), and Imbs and Mejean (2017) also consider Cobb–Douglas aggregations across sectors.

6 This is in contrast with studies such as by Bertoletti et al. (2018) or Arkolakis et al. (2018) who consider nonhomothetic preferences that cannot be distinguished in terms of income and substitution effects.

7 As shown by Hanoch (1975) and Comin et al. (2015), for all i, n, the utility function is well defined if ${\epsilon }_i<{\theta }_n$ when ${\theta }_n>1$, and if ${\epsilon }_i>{\theta }_n$ when $0<{\theta }_n<1$, corresponding to a globally monotonically increasing and quasi-concave $C_{nt}$.

8 The average of ${\lambda }_{nnt}$'s between 1995–2015 can be found in Appendix Table A2.

9 For sure, this identification strategy directly depends on the model introduced, where productivity measures are independent of trade costs.

10 The selected instruments are supported by the R-squared value of 0.332 in the first-stage regression and the corresponding test results suggesting that the null hypotheses of underidentification, weak identification and overidentification are all rejected.

11 A similar comparison is also included in the Appendix Table A2 according to the following expression: $\mathrm{\%}\mathrm{Bias}\mathrm{in}\mathrm{Welfare}\mathrm{Gains}=100\times (\underset{\mathrm{Biased}(\mathrm{Common})}{\underbrace{\frac{\log {\lambda }_{nn}}{{\epsilon }_n-\theta }}}-\underset{\mathrm{Unbiased}(\mathrm{Benchmark})}{\underbrace{\frac{\log {\lambda }_{nn}}{{\epsilon }_n-{\theta }_n}}})$where the unbiased (benchmark) gains from trade are compared to the biased gains based on having country-specific income elasticity measures together with a common trade elasticity across countries.

12 For robustness, when ${\gamma }_n$ is measured by population share of country n in the world population, the percentage global welfare gains of $8.38\mathrm{\%}$ and $6.70\mathrm{\%}$ are replaced by $7.18\mathrm{\%}$ and $6.56\mathrm{\%}$, respectively.

Additional information

Notes on contributors

Hakan Yilmazkuday

Hakan Yilmazkuday is a professor of economics at Steven J. Green School of International and Public Affairs, Florida International University.