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International transmission of productivity shocks with nonzero net foreign debt

Olena Mykhaylova and James Staveley-O’Carroll

Abstract

We study the impact of foreign debt on transmission of productivity shocks and on international risk sharing in a two-country DSGE model with incomplete asset markets and deviations from the purchasing power parity. We elucidate two channels through which debt affects international shock transmission. First, changes in domestic output cause fluctuations in the debt-to-GDP ratio and thus affect the risk premium on foreign borrowing. Second, fluctuations in the real exchange rate alter the real value of existing liabilities, generating wealth effects for the consumers in the indebted economy. Together, these two channels help to address the Backus-Smith puzzle by producing a negative consumption-real exchange rate correlation in an environment driven by productivity shocks. Our findings are robust to monetary policy rule specification but depend critically on the currency of debt denomination.

JEL classification: F32; F41; F44

Corresponding author: Olena Mykhaylova, Department of Economics, Robins School of Business, 28 Westhampton Way, University of Richmond, VA 23173, USA, e-mail:

Appendix A: A Model solution

A.1 Firms

The optimal price for an intermediate good variety is given by

P˜H,t=σintσint1Etj=t(αintβ)jtλjPH,jσintYH,jMCjEtj=t(αintβ)jtλjPH,jσintYH,j,

where MCt is the nominal marginal cost of production:

MCt=RtνWt1νZtνν(1ν)1ν

We consider a symmetric equilibrium in which every firm that gets a chance to reset its prices in period t will set it to the same value; therefore, optimal prices are not denoted by a firm subscript f. Given the price-setting behavior of individual firms, the aggregate price index of the composite intermediate good can be written as

PH,t1σint=(1αint)P˜H,t1σint+αintPH,t11σint

Analogously, each final good variety producer finds it optimal to charge

P˜t(i)=σfσf1Etj=tλj(αfβ)jtPjσfYjMCFjEtj=tλj(αfβ)jtPjσfYj

where Pt=[01Pt(i)1σfdi]11σf, and MCFt captures the marginal cost of inputs:

MCFt=[μPH,t1η+(1μ)(StPF,t)1η]11η.

A.2 Households

The demand for household h’s labor services, given its wage, is

Lt(h)=[Wt(h)Wt]σlLtM

Lt=M11σl[0MLt(h)σl1σldh]σlσl1

Wt=M1σl1[0MWt(h)1σldh]11σl,

where the last equation presents the aggregate wage level. The scaling factor M11σl is necessary to maintain the aggregate relationship Lt=01Lt(f)df=MLt(h). Together with the expression Kt=MKt(h) this will ensure that the production function exhibits constant returns to scale. Additionally, in the steady state, the aggregate wage W will equal the individual wage W(h).

For simplicity, in the equations below we drop the household subscript h.

λt=1CtΘPt11+it=βEt[(Ct+1Ct)ΘPtPt+1]11+it+φt=βEt[(Ct+1Ct)ΘΔSt+1PtPt+1]{1+ψ[KtKt11]}=βEt[Ct+1Ct]Θ{1δ+Rt+1+ψ2[(Kt+1Kt)21]}CH,t=μ[PH,tPt]ηCt,CF,t=(1μ)[StPF,tPt]ηCt

Here it is the yield on the one-period nominal risk-free bond, which can be easily derived from the set of state-contingent bonds Dt. Following Cochrane (2001), chapter 3, let p(D)=∑spc(s)D(s) be the price of a portfolio D of state-contingent bonds; here s’s denote states of nature, pc(s) is the price of a bond that pays one dollar next period contingent on the state s occurring, and D(s) is the number of such claims in portfolio D. If π(s) is the probability of state s, p(D)=∑sπ(s)[pc(s)/π(s)]D(s)=Ett,t+1Dt], where Δt,t+1 is the stochastic discount factor. Now consider a bond that costs 1 dollar in period t and pays I dollars in all states in t+1. We then can write It=1/Et,t+1) and let it≡lnIt.

We assume that every household which chooses its wage in period t sets it to the same new value:

W˜tσlχ+1=σlσl1Etj=t(αwβ)jtWjσl(χ+1)Lj1+χEtj=t(αwβ)jtλjWjσlLj

Similar to the derivations of the aggregate price level given firms’ first-order conditions, the aggregate wage level is given by

Wt1σl=(1αw)W˜t1σl+αwWt11σl

A.3 Derivation of the risk premium channel

To derive equation (23) highlighting the risk premium channel, we log-linearize the risk premium definition (13) to obtain

(32)ϕ^t=ϕ¯+1ϕ¯[ln(φ¯+1)+κ](q^t+d^tp^H,ty^t), (32)

where bars over variables denotes their steady state levels, and lower-case letters denote log-deviations of variables from the steady state. We next combine the log-linearized expressions for the two CPIs,

(33)0=μpH¯1ηp^H,t+(1μ)(Q¯pF¯)1η(p^F,t+q^t) (33)
(34)0=μ(Q¯pF¯)1ηp^F,t+(1μ)pH¯1η(p^H,tq^t), (34)

with the terms of trade expression τ^t=q^t+p^F,tp^H,t to get

(35)p^H,t=(1μ)τ¯1ημ+(1μ)τ¯1ητ^t (35)
(36)p^F,t=(1μ)τ¯η1μ+(1μ)τ¯η1τ^t (36)
(37)q^t=[1(1μ)τ¯η1μ+(1μ)τ¯η1(1μ)τ¯1ημ+(1μ)τ¯1η]τ^t (37)

Finally, by combining (35) and (37) with (32), we obtain

(38)φ^t=φ¯+1φ¯[ln(φ¯+1)+ξκ](μμ+(1μ)τ¯η1τ^t+d^ty^t) (38)

Since in the steady state τ¯1 and ln(φ¯+1)φ¯, the last expression simplifies to yield equation (23) in the main text.

B Data sources and description

B.1 Calibration

Unless otherwise indicated, all data are taken from OECD.Stat database and refer to the 1980Q1–2011Q3 period (or the earliest available date following 1980) variables in Czech Republic, Estonia, Hungary, Poland, Russian Federation, Slovak Republic, and Slovenia.

  • Pt: Consumer prices, all items, 2005=100

  • Yt: Gross domestic product, current prices, deflated by Pt

  • Ct: Private final consumption expenditure, current prices, deflated by the Pt

  • It: Gross fixed capital formation, current prices, deflated by the Pt

  • CAt: Current account balance, percent of GDP

  • Gt: General government final consumption expenditure, deflated by the Pt

  • πt: Inflation rate, calculated as log(Pt/Pt–1)

  • NFWt: Net foreign assets (Lane and Milesi-Ferretti, EWN II update for the web, August 2009); annual data for the 1970–2007 period

  • Qt: Bank for International Settlements effective real exchange rate index

B.2 Empirical exercises

Sample countries (155): Albania, Algeria, Argentina, Armenia, Australia, Austria, Azerbaijan, Bangladesh, Belarus, Belgium, Benin, Bolivia, Botswana, Brazil, Burkina Faso, Cambodia, Cameroon, Canada, Chad, Chile, China, Colombia, Congo, Republic of, Côte d’Ivoire, Croatia, Czech Republic, Denmark, Dominican Republic, Egypt, El Salvador, Equatorial Guinea, Estonia, Ethiopia, Fiji, Finland, France, Gabon, Georgia, Germany, Ghana, Greece, Guatemala, Guinea, Haiti, Honduras, Hong Kong, Hungary, Iceland, India, Indonesia, Iran, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kazakhstan, Kenya, Kyrgyz Republic, Latvia, Lithuania, Macedonia, Madagascar, Malawi, Malaysia, Mali, Mexico, Moldova, Morocco, Mozambique, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Nigeria, Norway, Oman, Pakistan, Papua New Guinea, Paraguay, Peru, Philippines, Poland, Portugal, Romania, Russia, Rwanda, Senegal, Singapore, Slovak Republic, Slovenia, South Africa, South Korea, Spain, Sri Lanka, Sweden, Switzerland, Syrian Arab Republic, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, Uganda, Ukraine, UK, US, Uruguay, Venezuela, Vietnam, Yemen, Zambia.

Unless otherwise indicated, all data are taken from IMF’s International Financial Statistics database and refer to the 1990–2004 period.

  • Pti: Consumer Prices, All Items. Index, 2005=100

  • Nti: Population (source: Penn World Table Version 7.1, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, November 2012)

  • Yti: Nominal Gross Domestic Product, deflated by Pti and Nti

  • Cti: Nominal Household Consumption Expenditure, incl. NPISHs, deflated by Pti and Nti

  • NFDRtij: Total Liabilities in Currency j as% of GDP less Total Assets in Currency j as % of GDP (source: Lane and Shambaugh 2010). Here j={USD, GBP, EUR, JPY, CHF}

  • Sti,USD: National Currency per US Dollar, period average

  • Qti,j: real exchange rate, computed as

    Qti,j=Sti,USDStj,USDPtjPti

Notes: CPI data (Index, 2005=100) for Azerbaijan, Belarus, and China are taken from World Bank World Development Indicators. Missing CPI data for Guinea, Oman, and Venezuela are replaced by GDP deflator (source: World Bank WDI). Consumption data for Croatia (Final Consumption Expenditure) are taken from EuroStat. GDP for Macedonia is taken from World Bank WDI. Eurozone data for the 1990–1994 period are calculated from individual 11 member states observations obtained from IFS, WDI, and EuroStat.

Table 6 shows the descriptive statistics of the data used in the regression analysis.

The 15 countries excluded in Panel B of Table 5: Australia, Brazil, Canada, China, France, Germany, India, Italy, Japan, Mexico, Netherlands, South Korea, Spain, UK, and the USA.

Table 6

Summary statistics.

VariableObs

(i)
Mean

(ii)
St. Dev.

(iii)
Min

(iv)
Max

(v)
Panel 1: vis-à-vis US
ΔlnYtiΔlnYtUS7830.01610.1227–0.34632.5222
ΔlnCtiΔlnCtUS7740.00810.1102–0.97541.6703
ΔlnQti,US787–0.00440.1570–1.86660.8128
NFDRti,US7689.666734.4997–132.0530170.4888
Panel 2: vis-à-vis UK
ΔlnYtiΔlnYtUK1510–0.00080.1031–0.52202.5462
ΔlnCtiΔlnCtUK1501–0.00890.1074–0.992001.6634
ΔlnQti,UK15120.00410.1644–2.02822.6375
NFDRti,UK1489–2.07997.8248–85.8420.9611
Panel 3: vis-à-vis Euro
ΔlnYtiΔlnYtEuro11080.01250.1080–0.48032.4743
ΔlnCtiΔlnCtEuro1103–0.00070.1101–0.59421.4846
ΔlnQti,Euro11110.00140.1796–1.96262.7030
NFDRti,Euro1085–0.343115.1674–105.970084.2443
Panel 4: vis-à-vis Japan
ΔlnYtiΔlnYtJp15100.02580.1020–0.48652.5000
ΔlnCtiΔlnCtJp15010.01510.1066–0.96701.6354
ΔlnQti,Jp15120.00080.1850–1.75302.9126
NFDRti,Jp14895.34948.5961–20.928962.5846
Panel 5: vis-à-vis Switzerland
ΔlnYtiΔlnYtSw15100.02660.1022–0.47632.5485
ΔlnCtiΔlnCtSw15010.01820.1056–0.95651.6486
ΔlnQti,Sw15120.00190.1651–1.91312.7525
NFDRti,Sw1489–0.34462.2708–13.865215.4817
Panel 6: full sample
ΔlnYtiΔlnYtj64210.01630.1066–0.52202.5485
ΔlnCtiΔlnCtj63800.00660.1081–0.99201.6703
ΔlnQti,j64340.00130.1714–2.02822.9126
NFDRti,j63201.804915.2603–132.0530170.4888

Summary statistics for the dataset used in Section 5. Panels 1–5 describe the variables relative to the five interational currencies, and panel 6 includes the entire set. Negative values of NFDRt indicate countries with above-zero levels of net foreign wealth.

C Additional robustness checks

The model assumes that the home economy is characterized by a Taylor rule while the foreign country pursues the policy of strict inflation targeting. This specification is useful for the SOE analysis of Section 4.6; it is common in the literature to assume that the small open economy does not influence the rest of the world (in our model represented by the foreign country), which typically follows the policy of strict inflation targeting.[21] However, to check that the results of our paper – especially of the first several sections in which both economies are of equal size – do not hinge on this asymmetric specification, below we present the consumption-RER correlations when both monetary policies are symmetric. In Panel A, we assume that both countries follow the Taylor rule described by (15) when prices and wages are sticky, while in Panel B home and foreign central banks set π=π*=0 at all times (in this latter case the results are independent of the degree of nominal rigidity).

As is evident from the last column of Table 7, our main channels are virtually unaffected by the monetary policy specification. Interestingly, the same anomaly described in Section 4.2 appears in the Panel A setup as well: low trade elasticity combined with high debt level fails to generate a negative RER-consumption correlation following a home productivity shock. The explanation of this phenomenon is the same as before, however. Switching from π*=0 to a Taylor rule significantly increases the volatility of the foreign (and consequently home) price level; more volatile prices create a larger RER depreciation through the debt valuation channel, which cannot be fully offset by the risk premium channel and the feedback loop.

Table 7

Effects of monetary policy rules.

Corr (q, cc*)NFDR=0NFDR=1
η=0.75

(i)
η=1.5

(ii)
η=0.75

(iii)
η=1.5

(iv)
Panel A: Both Taylor rules
 Home productivity–0.860.980.74–0.87
 Foreign productivity–0.900.99–0.17–0.30
 Unconditional correlation–0.850.99–0.07–0.67
Panel B: Both inflation targeting
 Home productivity–0.560.99–0.87–0.90
 Foreign productivity–0.800.97–0.44–0.57
 Unconditional correlation–0.640.98–0.55–0.75

Consumption-real exchange rate correlation under different policy rules. Unconditional correlation refers to the model specification in which both home and foreign productivity shocks operate at the same time.

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Published Online: 2014-8-13
Published in Print: 2014-1-1

©2014 by De Gruyter

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