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Implications of Exchange Rate Pass-Through and Nontradable Goods for International Policy Cooperation

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Abstract

This paper investigates the welfare consequences of international policy cooperation by simultaneously introducing the following three elements in a standard two-country general equilibrium model: (i) general degrees of exchange rate pass-through, (ii) nontradable goods and their sector-specific productivity shocks, and (iii) general weights on goods in Cobb–Douglas consumption indices. There are two channels for possible mutual welfare gains from policy cooperation: First, cooperation can compensate for insufficient changes in the terms of trade when the degree of exchange rate pass-through is intermediate. Second, countries can cooperate in reaction to shocks in the nontradable goods sectors. This second channel is revealed by deriving an analytical condition for welfare gains under full pass-through and this condition is characterized by the weights in the consumption indices and the variances of sector-specific productivity shocks. Numerical evaluation demonstrates that when the two countries are symmetric and equal weights on consumption goods are assumed, welfare gains from cooperation increase as symmetric pass-through elasticity increases, which implies that the second channel dominates the first, whose effect on welfare gains is nonmonotonic in pass-through elasticity.

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Notes

  1. This paper defines such a pricing framework as vehicle currency pricing, motivated by Goldberg and Tille (2008, 2009), who point out that vehicle currency is prominently used in international trade.

  2. Throughout the paper, intermediate pass-through is defined as pass-through elasticity that is strictly positive and less than one.

  3. In a more general formulation (e.g. Benigno and Benigno (2003), Duarte and Stockman (2005), and Corsetti et al. (2008)), the tradable good consumption index is given by a CES (constant elasticity of substitution) function. Letting the elasticity of substitution between Home and Foreign traded goods equal to one gives Eq. 3.

  4. The derivation follows Corsetti and Pesenti (2004). Note that γ = 1 − γ ∗ and ϕ = ϕ ∗ are assumed in their derivation. As pointed out by Corsetti and Pesenti (2005), the balanced equilibrium current account relies on the following three assumptions: (i) the Cobb–Douglas consumption indices, (ii) the logarithmic utility function of consumption, and (iii) zero initial non-monetary wealth.

  5. If a complete market is assumed, as in Devereux and Engel (2003) and Devereux et al. (2007), the marginal utility from nominal spending is equalized across countries, up to a weighting constant. One can see that risk sharing is attained in the model with a weighting constant \(\frac {(1-\gamma )\phi }{(1-\gamma ^{*})\phi ^{*}}\), although the model does not assume a complete market. Note that this constant is equal to unity if the two countries’ consumption indices are symmetric, that is, if γ = γ ∗ and ϕ = ϕ ∗.

  6. See, for example, Devereux and Engel (2003), Devereux et al. (2003), Corsetti and Pesenti (2005), and Duarte and Obstfeld (2008).

  7. For the Home country, \(\int _{0}^{1}(M_{t}(j)-M_{t-1}(j))dj + \int _{0}^{1}\mathcal {T}_{t}(j)dj = 0\). The Foreign counterpart is analogous.

  8. See, for example, Obstfeld and Rogoff (2000), Corsetti and Pesenti (2001), Devereux and Engel (2003), and Goldberg and Tille (2009).

  9. See the Appendix for the closed-form expressions of the welfare functions.

  10. Recall that the Home (Foreign) country’s welfare is W ( W ∗) plus additional terms. Since the additional terms do not depend on policy rules, they cancel each other out and do not appear in the equation for welfare gains.

  11. Note that the intuition for the Foreign country is similar.

  12. Suppose, for now, that technology shocks are countrywide in both countries and that the shocks in the tradable and nontradable goods sectors are identical, as in Obstfeld and Rogoff (2002). In this situation, monetary policy responses under cooperation coincide with those under noncooperation, since \(\xi _{1}^C+\xi _{2}^{C} = \xi _{1}^{N} + \xi _{2}^{N}\), \(\xi _{3}^C+\xi _{4}^{C} = \xi _{3}^{N} + \xi _{4}^{N}\), and the same relations for ψ.

  13. Another extreme case with no gains from cooperation is when ϕ = ϕ ∗ = 0. In this case, the two countries are completely separate economies and there are obviously no gains from cooperation.

  14. This condition is imposed in the numerical experiment in Section 4.2.

  15. Such a currency is defined as the vehicle currency, following Goldberg and Tille (2008, 2009).

  16. The results are not sensitive to the value of symmetric variances. Setting \(\sigma _{u_{\mathrm {N}}}^{2} = \sigma _{u_{\mathrm {N}}^{*}}^{2} = 1\) and \(\sigma _{u_{\mathrm {N}}}^{2} = \sigma _{u_{\mathrm {N}}^{*}}^{2} = 0.1\) leads to similar results.

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Authors and Affiliations

  1. National Taiwan University, 21 Hsu-Chow Road, Taipei, 100, Taiwan

    Masanori Kashiwagi

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  1. Masanori Kashiwagi
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Correspondence to Masanori Kashiwagi.

Additional information

For helpful comments, I thank George Tavlas (Editor), an anonymous referee, Nan-Kuang Chen, Biing-Shen Kuo, Wei-Wei Lee, Yiting Li, Guillaume Rocheteau, Hung-Jen Wang and seminar participants at National Taiwan University, National Chengchi University, National Chung Cheng University, the ASSA (CEANA-NTU-TEA Session) in San Diego, and the Singapore Economic Review Conference. Financial support from the National Science Council is gratefully acknowledged.

Appendix

Appendix

This appendix describes the welfare functions for both countries. As in the text, W and W ∗ denote the Home and Foreign welfare functions, respectively. Due to the properties of the model, these welfare functions can be described in closed form, following an approach taken by Devereux and Engel (2003). For the sake of brevity, I provide only the welfare functions below.

The Home welfare function is given by

$$\begin{array}{rll} \mathcal{W} = &-& \frac{\sigma_{c}^{2}}{2} -\frac{\eta^{2} (1-\gamma) \phi \left(1- (1-\gamma) \phi \right)}{2} \sigma_{e}^2 + \gamma \phi \sigma_{cu_{\mathrm{T}} } + (1-\gamma) \phi \sigma_{cu_{\mathrm{T}} ^{*}}\notag \\ &+& (1-\phi) \sigma_{cu_{\mathrm{N}} } + \eta \gamma (1-\gamma ) \phi^{2} \sigma_{eu_{\mathrm{T}} } - \eta (1-\gamma) \phi \left(1 - (1-\gamma) \phi \right) \sigma_{eu_{\mathrm{T}} ^{*}}\notag\\ &+& \eta (1-\gamma) \phi (1-\phi) \sigma_{eu_{\mathrm{N}} }, \end{array} $$

where lowercase letters denote the log of the corresponding variables (i.e. c ≡ lnC and \(e \equiv \ln \mathcal {E}\)) and σ x y denotes the covariance between x and y. The second moments are given by

$$\begin{array}{rll} &&\sigma_{c}^{2} = \left[ \left(1- \eta (1-\gamma) \phi \right) \xi_{1} + \eta (1-\gamma) \phi \psi_{1} \right] ^2 \sigma_{u_{\mathrm{T}} }^{2}\notag\\ &&{\kern2pc} + \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_2+ \eta (1-\gamma)\phi\psi_{2} \right]^{2}\sigma_{u_{\mathrm{N}} }^{2} \notag\\ &&{\kern2pc}+ \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_3+ \eta (1-\gamma)\phi\psi_{3} \right]^{2}\sigma_{u_{\mathrm{T}} ^{*}}^{2}\notag\\ &&{\kern2pc}+ \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_4+ \eta (1-\gamma)\phi\psi_{4} \right]^{2}\sigma_{u_{\mathrm{N}} ^{*}}^{2},\notag\\ &&{\kern-.1pc}\sigma_{e}^{2} = (\xi_1-\psi_1)^{2} \sigma_{u_{\mathrm{T}} }^2 + (\xi_2-\psi_2)^{2} \sigma_{u_{\mathrm{N}} }^2 + (\xi_3-\psi_3)^{2} \sigma_{u_{\mathrm{T}} ^{*}}^2 + (\xi_4-\psi_4)^{2} \sigma_{u_{\mathrm{N}} ^{*}}^{2}, \\ &&{\kern-.7pc}\sigma_{cu_{\mathrm{T}} } = \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_1+ \eta (1-\gamma)\phi\psi_{1} \right] \sigma_{u_{\mathrm{T}} }^{2}, \\ &&{\kern-.75pc}\sigma_{cu_{\mathrm{N}} } = \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_2+ \eta (1-\gamma)\phi\psi_{2} \right] \sigma_{u_{\mathrm{N}} }^{2}, \\ &&{\kern-.75pc}\sigma_{cu_{\mathrm{T}} ^{*}} = \left[ \left(1- \eta (1-\gamma)\phi \right) \xi_3+ \eta (1-\gamma)\phi\psi_{3} \right] \sigma_{u_{\mathrm{T}} ^{*}}^{2}, \\ &&{\kern-.75pc}\sigma_{eu_{\mathrm{T}} } = (\xi_1-\psi_1)\sigma_{u_{\mathrm{T}} }^{2}, \\ &&{\kern-.75pc}\sigma_{eu_{\mathrm{N}} } = (\xi_2-\psi_2)\sigma_{u_{\mathrm{N}} }^{2}, \\ &&{\kern-.75pc}\sigma_{eu_{\mathrm{T}} ^{*}} = (\xi_3-\psi_3)\sigma_{u_{\mathrm{T}} ^{*}}^2. \end{array} $$

Similarly, the Foreign welfare function is given by

$$\begin{array}{rll} \mathcal{W}^{*} = &-& \frac{\sigma_{c^{*}}^{2}}{2} -\frac{ (\eta^{*})^{2} (1-\gamma^{*}) \phi^{*} \left( 1- (1-\gamma^{*}) \phi^{*} \right)}{2}\sigma_{e}^{2} \notag\\ &+& (1-\gamma^{*}) \phi^{*} \sigma_{c^{*} u_{\mathrm{T}} } + \gamma^{*} \phi^{*} \sigma_{c^{*}u_{\mathrm{T}} ^{*}} + (1-\phi^{*}) \sigma_{c^{*} u_{\mathrm{N}}^{*} } \notag \\ &+& \eta^{*} (1-\gamma^{*}) \phi^{*} (1-(1-\gamma^{*})\phi^{*} ) \sigma_{eu_{\mathrm{T}} } - \eta^{*} \gamma^{*}(1-\gamma^{*}) (\phi^{*})^{2} \sigma_{eu_{\mathrm{T}} ^{*}} \notag\\ &-& \eta^{*} (1-\gamma^{*}) \phi^{*} (1-\phi^{*}) \sigma_{eu^{*}_{\mathrm{N}} }, \end{array} $$

where the second moments are given by

$$\begin{array}{rll} \sigma_{c^{*}}^{2} &=& \left[\eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{1} + \left(1- \eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{1} \right] ^2 \sigma_{u_{\mathrm{T}} }^{2} \notag\\ &&{\kern5pt} + \left[\eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{2} + \left(1-\eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{2} \right]^{2}\sigma_{u_{\mathrm{N}} }^{2} \\ &&{\kern5pt} + \left[ \eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{3} + \left(1- \eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{3} \right]^{2}\sigma_{u_{\mathrm{T}} ^{*}}^{2} \\ &&{\kern5pt} + \left[\eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{4} + \left(1-\eta^{*} (1-\gamma^{*}) \phi^{*}\right) \psi_{4} \right]^{2}\sigma_{u_{\mathrm{N}} ^{*}}^{2}, \\ \sigma_{e}^{2} &=& (\xi_1-\psi_1)^{2} \sigma_{u_{\mathrm{T}} }^2 + (\xi_2-\psi_2)^{2} \sigma_{u_{\mathrm{N}} }^2 + (\xi_3-\psi_3)^{2} \sigma_{u_{\mathrm{T}} ^{*}}^2 + (\xi_4-\psi_4)^{2} \sigma_{u_{\mathrm{N}} ^{*}}^{2}, \\ \sigma_{c^{*}u_{\mathrm{T}} } &=& \left[ \eta^{*} (1-\gamma^{*}) \phi^{*} \xi_1+ \left(1-\eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{1} \right] \sigma_{u_{\mathrm{T}} }^{2}, \\ \sigma_{c^{*}u_{\mathrm{T}} ^{*}} &=& \left[\eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{3} + \left(1-\eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{3} \right] \sigma_{u_{\mathrm{T}} ^{*}}^{2}, \end{array} $$
$$\begin{array}{rll} \sigma_{c^{*}u_{\mathrm{N}} } &=& \left[\eta^{*} (1-\gamma^{*}) \phi^{*} \xi_{4} + \left(1- \eta^{*} (1-\gamma^{*}) \phi^{*} \right) \psi_{4} \right] \sigma_{u^{*}_{\mathrm{N}} }^{2}, \\ \sigma_{eu_{\mathrm{T}} } &=& (\xi_1-\psi_1)\sigma_{u_{\mathrm{T}} }^{2}, \\ \sigma_{eu_{\mathrm{T}} ^{*}} &=& (\xi_3-\psi_3)\sigma_{u_{\mathrm{T}} ^{*}}^{2}, \\ \sigma_{eu_{\mathrm{N}}^{*} } &=& (\xi_4-\psi_4)\sigma_{u_{\mathrm{N}}^{*} }^2. \end{array} $$

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Kashiwagi, M. Implications of Exchange Rate Pass-Through and Nontradable Goods for International Policy Cooperation. Open Econ Rev 25, 771–795 (2014). https://doi.org/10.1007/s11079-013-9306-4

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