Skip to main content
Log in

Real Adjustment of Current Account Imbalances with Firm Heterogeneity

  • Published:
IMF Economic Review Aims and scope Submit manuscript

Abstract

In this paper, a standard model of international transfer is augmented by the introduction of firm heterogeneity. The increase in aggregate exports in response to the transfer reflects extensive and intensive adjustments, as the sales of new exporting firms (extensive margin) contribute to the current account adjustment along with the sales of existing exporting firms (intensive margin). The relative size of the intensive and extensive margins of the adjustment is determined by the size dispersion of firms. The model calibrated to the observed distribution of firm sizes shows that the intensive margin is the predominant channel of the current account adjustment. The dampening effect of the extensive margin has therefore very little impact on the exchange rate adjustment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Hummels and Klenow (2005) find that larger countries trade more and the extensive margin can account for 60 percent of the difference in trade flows. Galstyan and Lane (2008) show that around half of U.S. trade growth has occurred at the extensive margin over a relatively short period of time (2000–2004).

  2. In their multilateral model calibrated to 40 countries using 2004 data on GDP and bilateral trade, Dekle, Eaton, and Kortum (2008) show that the wage of the largest deficit country (United States) falls by 10 percent relative to the largest surplus country (Japan).

  3. This channel has been widely analyzed in Lane and Milesi-Ferretti (2007), Gourinchas and Rey (2007a and 2007b), and Curcuru, Dvorak, and Warnock (2008).

  4. In a similar way, the profits for Foreign firms are πF,T*(x)=πF,D*(x)+(1/ɛ)πF,  EXP (x), and πF,N*(x) where: πF,D*(x)=(1/σ)[(pF,D*(x))/P T *]1−σP T *CF,  T FF,  D if the firm is active on the domestic market, and 0 otherwise; πF,  EXP (x)=(1/σ)[(ɛpF,  EXP *(x))/P T ]1−σP T CH,  T −ɛFF,  EXP if the firm exports, and 0 otherwise; πF,N*(x)=(1/σ)[(pF,N*(x))/P N *]1−σP N *CF,  N FF,  D if the firm is active in the nontradable good sector, and 0 otherwise.

  5. This assumption on the shape parameter γ and elasticity σ ensures a finite mean for the sales of the firms.

  6. A similar equation holds true for the Foreign country: P*C F =L F (γσ/γσ−σ+1)+T/ɛ.

  7. See the Appendix for the calculation of the productivity thresholds at the symmetrical equilibrium, when the nontradable sector is shut down.

  8. B=[(τ(1−σ)ψFH,  EXP )1−ψ)/((σFH,  D )1−ψ(1−σ)ψFH,  EXP )1−ψ)] and A=[(τ(1−σ)ψ × (σFH,  EXP )1−ψ)/B].

  9. Note that ψ=γ/(σ−1)>1 as γ>σ−1 by assumption.

  10. C=((A−1)/A)+(ψσ/ψσ−1).

  11. , where d(x)=σ[πH,  D (x)+FH,  D ].

  12. This value is equal to U.S. imports from the rest of the world in 2009 (about $1,946 billion) divided by world GDP excluding United States in 2009 (about $58,141 billion minus $14,119 billion) according to WDI data.

  13. See the Appendix for the numerical decomposition of the two margins.

  14. Notice that for an elasticity of substitution of 2, the exchange rate depreciation of the model without extensive margin raises to 8.4 percent. For a larger current account adjustment (deficit equal to 5 percent instead of 2.7 percent of Home GDP), the required depreciation in the model without extensive margin amounts to 15 percent.

  15. The exchange rate depreciation is slightly affected by the productivity dispersion of firms because of approximation errors.

References

  • Arkolakis, Costas, Arnaud Costinot, and Andrés Rodríguez-Clare, 2009, “New Trade Models, Same Old Gains?” NBER Working Papers 15628 (National Bureau of Economic Research, Inc).

  • Axtell, Robert L., 2001, “Plants and Productivity in International Trade,” Science, Vol. 293, No. 5536, pp. 1818–1820.

    Article  Google Scholar 

  • Bernard, Andrew B., Jonathan Eaton, J. Bradford Jensen, and Samuel Kortum, 2003, “Plants and Productivity in International Trade,” American Economic Review, Vol. 93, No. 4, pp. 1268–1290.

    Article  Google Scholar 

  • Chaney, Thomas, 2008, “Distorted Gravity: The Intensive and Extensive Margins of International Trade,” American Economic Review, Vol. 98, No. 4, pp. 1707–1721.

    Article  Google Scholar 

  • Corsetti, Giancarlo, Philippe Martin, and Paolo Pesenti, 2008, “Varieties and the Transfer Problem: The Extensive Margin of Current Account Adjustment,” CEPR Discussion Papers 6660, C.E.P.R. Discussion Papers.

  • Curcuru, Stephanie E., Tomas Dvorak, and Francis E. Warnock, 2008, “Cross-Border Returns Differentials,” Quarterly Journal of Economics, Vol. 123, No. 4, pp. 1495–1530.

    Article  Google Scholar 

  • Dekle, Robert, Jonathan Eaton, and Samuel Kortum, 2008, “Global Rebalancing with Gravity: Measuring the Burden of Adjustment,” IMF Staff Papers, Vol. 55, No. 3, pp. 511–540.

    Article  Google Scholar 

  • Galstyan, Vahagn, and Philip R. Lane, 2008, “External Imbalances and the Extensive Margin of Trade,” Economic Notes, Vol. 37, No. 3, pp. 241–257.

    Article  Google Scholar 

  • Ghironi, Fabio, and Marc J. Melitz, 2005, “International Trade and Macroeconomic Dynamics with Heterogeneous Firms,” The Quarterly Journal of Economics, Vol. 120, No. 3, pp. 865–915.

    Google Scholar 

  • Gourinchas, Pierre-Olivier, and Hélène Rey, 2007a, “From World Banker to World Venture Capitalist: U.s. External Adjustment and the Exorbitant Privilege,” in G-7 Current Account Imbalances: Sustainability and Adjustment, ed. by Clarida, R. (Chicago: The University of Chicago Press), pp. 11–55.

    Chapter  Google Scholar 

  • Gourinchas, Pierre-Olivier, and Hélène Rey, 2007b, “International Financial Adjustment,” Journal of Political Economy, Vol. 115, No. 4, pp. 665–703.

    Article  Google Scholar 

  • Hummels, David, and Peter J. Klenow, 2005, “The Variety and Quality of a Nation's Exports,” American Economic Review, Vol. 95, No. 3, pp. 704–723.

    Article  Google Scholar 

  • Imbs, Jean, and Isabelle Mejean, 2009, “Elasticity Optimism,” CEPR Discussion Papers 7177, C.E.P.R. Discussion Papers.

  • Lane, Philip R., and Gian Maria Milesi-Ferretti, 2007, “The External Wealth of Nations Mark ii: Revised and Extended Estimates of Foreign Assets and Liabilities, 1970–2004,” Journal of International Economics, Vol. 73, No. 2, pp. 223–250.

    Article  Google Scholar 

  • Levchenko, Andrei A., Julian di Giovanni, and Romain Rancière, 2010, “Power Laws in Firm Size and Openness to Trade: Measurement and Implications,” IMF Working Papers 10/109 (International Monetary Fund).

  • Melitz, Marc J., 2003, “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity,” Econometrica, Vol. 71, No. 6, pp. 1695–1725.

    Article  Google Scholar 

  • Obstfeld, Maurice, and Kenneth Rogoff, 2001, “The Six Major Puzzles in International Macroeconomics: Is There a Common Cause?” in NBER Macroeconomics Annual 2000, ed. by Ben S. Bernanke and Kenneth Rogoff, Vol. 15, NBER Chapters, (National Bureau of Economic Research, Inc: MIT Press), pp. 339–412.

    Google Scholar 

  • Obstfeld, Maurice, and Kenneth S. Rogoff, 2005, “Global Current Account Imbalances and Exchange Rate Adjustments,” Brookings Papers on Economic Activity, Vol. 36, No. 2005–1, pp. 67–146.

    Article  Google Scholar 

Download references

Authors

Additional information

*Francesco Pappadà is a research fellow at CREST (INSEE) and Paris School of Economics. The author thanks seminar participants at the Paris School of Economics, University of Siena and CREST (INSEE), conference participants at RIEF Barcelona 2008, EEA Milan 2008 and T2M Strasbourg 2009, Nicolas Dromel, Jean-Olivier Hairault, Guy Laroque, Sophie Osotimehin, Julien Martin and especially Philippe Martin and Isabelle Méjean for their comments. The author is also grateful to two anonymous referees, and the editors, Pierre-Olivier Gourinchas and Ayhan Kose.

Appendix

Appendix

A.1. Productivity Thresholds at the Symmetrical Equilibrium

For sake of tractability, the nontradable sector is shut down by taking k=1, so that the aggregate expenditure in the Home country is PH, TCH, T=[L H (γσ/(γσ−σ+1))−T] Y H , whereas in the Foreign country it is PF, T*CF, T=[L F (γσ/(γσ−σ+1))+(T/ɛ)]≡Y F . Price indices are then P=P T and P*=P T *.

The zero-profit conditions (9), (10), (12), (13) provide the values of productivity thresholds for given price indices:

Plugging the productivity thresholds H, D and F, EXP into Equation (15), one can obtain the equilibrium value of the Home price index P. In a similar way, the equilibrium price index P*is obtained by plugging the thresholds F, D and H, EXP into Equation (17):

where μ=φ−γγ/γ−σ+1) is a constant.

Plugging the equilibrium price indices P and P* into the zero-profit conditions, one can get the productivity thresholds as functions of the exchange rate and fundamentals only.

Solving the model at the symmetrical equilibrium implies L H =L F , FH, D=FF, D, FH, EXP=FF, EXP, T=0 and ɛ=1. At the symmetrical equilibrium, the price indices are therefore

and the symmetrical equilibrium productivity thresholds are obtained by replacing these price indices into Equations (A.1), (A.2), (A.3) and (A.4).

A.2. Numerical Decomposition of the Extensive and the Intensive Margin

Define the vector of the initial equilibrium productivity thresholds =(H, D, H, N, H, EXP, F, D, F, N, F, EXP), and the vector of after-transfer equilibrium productivity thresholds ′. The current account position can be then written as a function of the transfer and the vector of equilibrium productivity thresholds: CA H (T, ). The change in the current account position due to the transfer of resources can be therefore decomposed as:

and the shares of the extensive and the intensive margin on the overall current account adjustment in Tables 2 and 3 are respectively:

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pappadà, F. Real Adjustment of Current Account Imbalances with Firm Heterogeneity. IMF Econ Rev 59, 431–454 (2011). https://doi.org/10.1057/imfer.2011.16

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/imfer.2011.16

JEL Classifications

Navigation