Technology shocks and current account dynamics ∗ Espen Henriksen University of Oslo Frederic Lambert † New York University March 2007 Abstract Despite success along some dimensions, international business cycle models have difficulty replicating several salient features of international capital flows among developed countries. In particular, net exports and current account balances are much more persistent in the data than in standard models. We account for this feature of the data with a simple one- good two-country model in which technology exhibits long run growth differences between the two countries. This specification implies persistent differences in per capita GDPs across countries, that are similar to what we observe among developed countries. Large and persistent trade balances arise as an optimal outcome of the model. JEL Classification Codes: F21, F32, E20. Keywords: net exports, current account, technology shocks. * We are especially grateful to David Backus, Mario Crucini and Julien Matheron for detailed comments. We also thank Cliff Hurvich, Fabrizio Perri, Matteo Pignatti, Victor Rios-Rull, Kjetil Storesletten, Daniel Volberg, and seminar participants at various institutions and conferences. † Corresponding author: Stern School of Business, 44 West 4th Street, Suite 7-176, New York, NY 10012 - tel: (212) 998-0881 - fax: (212) 995-4218 - fl[email protected]1
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Technology shocks and current account dynamics∗
Espen Henriksen
University of Oslo
Frederic Lambert†
New York University
March 2007
Abstract
Despite success along some dimensions, international business cycle models have difficulty
replicating several salient features of international capital flows among developed countries.
In particular, net exports and current account balances are much more persistent in the
data than in standard models. We account for this feature of the data with a simple one-
good two-country model in which technology exhibits long run growth differences between
the two countries. This specification implies persistent differences in per capita GDPs
across countries, that are similar to what we observe among developed countries. Large
and persistent trade balances arise as an optimal outcome of the model.
JEL Classification Codes: F21, F32, E20.
Keywords: net exports, current account, technology shocks.
∗We are especially grateful to David Backus, Mario Crucini and Julien Matheron for detailedcomments. We also thank Cliff Hurvich, Fabrizio Perri, Matteo Pignatti, Victor Rios-Rull, Kjetil
Storesletten, Daniel Volberg, and seminar participants at various institutions and conferences.†Corresponding author: Stern School of Business, 44 West 4th Street, Suite 7-176, New York,
where for notational concision we dropped the history-dependent notation. ni,t is
computed as the product of total employment and the average number of hours
worked per employee in the business sector (the average number of hours worked for
all sectors is generally not available). ki,t is approximated by the capital stock of the
business sector, excluding house building, in real terms. yi,t is real GDP. To allow
international comparisons of productivity levels, both capital stocks and GDP were
converted into US dollars. We use country-specific labor shares (1−α) computed by
Bernanke and Gurkaynak (2001). Except for labor shares data, all series come from
the OECD Main Economic Indicators, Economic Outlook or Quarterly National
Accounts databases.
Appendix B : Tools for the spectral analysis of time
series
Consider the covariance-stationary series {xt}n−1t=0 with mean x. The sample autocor-
relation at lag r is defined as the ratio of the autocovariance at lag r to the variance
of the series:
ˆacf r =crc0
(B-1)
where cr = 1n
∑n−1t=|r|(xt− x)(xt−|r|− x). This definition which corresponds to a biased
estimator of the autocovariance ensures that the sample autocorrelation lies between
-1 and 1. The periodogram is the Fourier transform of the sample autocovariance
sequence:
I(ωj) =1
2π
∑
|r|<n
cre−irωj (B-2)
19
where ωj = 2πj/n is the jth Fourier frequency. The periodogram integrates to the
sample variance:∫ π
−π
I(ω)dω = c0 (B-3)
It follows that the ordinate I(ωj) has a nice interpretation as the portion of the
sample variance due to the harmonic component at frequency ωj . Note that it can
be rewritten as:
I(ωj) =1
2π
[
c0 + 2
n−1∑
r=1
cr(eirωj + e−irωj)
]
=1
2π
[
c0 + 2
n−1∑
r=1
cr cos(ωjr)
]
(B-4)
The spectrum is obtained by smoothing the periodogram using a q-period Bartlett
window, where the choice of the bandwith parameter q results from a trade-off
between reducing the variance and minimizing the bias of the estimate. Then,
f(ωj) =1
2π
∑
|r|<q
(1 − |r|/q)cre−irωj
=1
2π
[
c0 + 2
q−1∑
r=1
(1 − |r|/q)cr cos(ωjr)
]
(B-5)
20
References
Aguiar, M. and G. Gopinath (2007). “Emerging market business cycles: The cycle
is the trend.” Journal of Political Economy, 115(1), 69–102.
Backus, D., E. Henriksen, F. Lambert and C. Telmer (2005). “Current account fact
and fiction.”
Backus, D. K., P. J. Kehoe and F. E. Kydland (1992). “International real business
cycles.” Journal of Political Economy, 100(4), 745–775.
Barro, R. J. and X. Sala-i Martin (1992). “Convergence.” Journal of Political
Economy, 100(2), 223–251.
Bassanini, A. and S. Scarpetta (2002). “The driving forces of economic growth:
Panel data evidence for the OECD countries.” OECD Economic Studies, 33.
Baxter, M. and M. J. Crucini (1993). “Explaining saving-investment correlations.”
American Economic Review, 83(3), 416–436.
Baxter, M. and M. J. Crucini (1995). “Business cycles and the asset structure of
foreign trade.” International Economic Review, 36(4), 821–854.
Bernanke, B. S. and R. S. Gurkaynak (2001). “Is growth exogenous? Taking
Mankiw, Romer and Weil seriously.” NBER Working Paper, (8365).
Box, G. and G. Jenkins (1970). Time Series Analysis, Forecasting and Control.
Holden Day, San Francisco.
Caballero, R. J., E. Farhi and P.-O. Gourinchas (2006). “An equilibrium model of
“global imbalances” and low interest rates.”
Campbell, J. Y. and N. G. Mankiw (1987). “Are output fluctuations transitory?”
The Quarterly Journal of Economics, 102(4), 857–80.
Cochrane, J. (1988). “How big is random walk in GDP?” Journal of Political
Economy, 96(5), 893–92.
Cogley, T. and J. M. Nason (1995). “Output dynamics in real-business-cycle mod-
els.” American Economic Review, 85(3), 492–511.
21
Diebold, F. and G. Rudebusch (1989). “Long memory and persistence in aggregate
output.” Journal of Monetary Economics, 24, 189–209.
Engel, C. and J. H. Rogers (2006). “The U.S. current account deficit and the
expected share of world output.” Journal of Monetary Economics, 53(5), 1063–
1093.
Fogli, A. and F. Perri (2006). “The ”great moderation” and the us external imbal-
ance.” NBER Working paper, (12708).
Hamilton, J. D. (1989). “A new approach to the economic analysis of nonstationary
time series and the business cycle.” Econometrica, 57, 357–384.
Heer, B. and A. Maussner (2004). “Projection methods and the curse of dimension-
ality.”
Lane, P. R. and G. M. Milesi-Ferretti (2006). “The external wealth of nations mark
II: Revised and extended estimates of foreign assets and liabilities, 1970-2004.”
IMF Working Paper.
McGrattan, E. R. (1999). “Application of weighted residual methods to dynamic eco-
nomic models.” In Computational Methods for the Study of Dynamic Economies.
Ramon Marimon and Andrew Scott.
Mendoza, E., V. Quadrini and J.-V. Rıos-Rull (2006). “Financial integration, finan-
cial deepness and global imbalances.”
Nelson, C. and C. Plosser (1982). “Trends and random walks in macroeconomic
time series.” Journal of Monetary Economics, 10, 139–162.
Quah, D. (1990). “Permanent and transitory movements in labor income: An ex-
planation for ‘excess smoothness’ in consumption.” Journal of Political Economy,
98, 449–475.
Sowell, F. (1992). “Maximum likelihood estimation of stationary univariate frac-
tionally integrated time series models.” Journal of Econometrics, 53, 165–188.
22
Stockman, A. C. and L. L. Tesar (1995). “Tastes and technology in a two-country
model of the business cycle: Explaining international comovements.” American
Economic Review, 85(1), 168–185.
Watson, M. W. (1993). “Measures of fit for calibrated models.” Journal of Political
Economy, 101(6), 1011–1041.
23
Table 1: Trade and current account balances in OECD countries
Trade balances in % of GDP (2005)
Largest deficits Largest surplusses
Iceland -12.4% Luxembourg 21.3%
Portugal -8.9% Norway 17.2%
Greece -7.2% Ireland 12.7%
Turkey -6.6% Sweden 7.7%
United States -5.8% Netherlands 7.7%
Spain -5.4% Switzerland 6.8%
Slovakia -5.1% Finland 5.6%
United Kingdom -3.7% Germany 5.2%
Current account balances in % of GDP (2005)
Largest deficits Largest surplusses
Iceland -16.5% Norway 15.5%
Portugal -9.2% Switzerland 15.3%
New Zealand -9.0% Luxembourg 11.8%
Slovakia -8.6% Netherlands 7.7%
Spain -7.4% Sweden 7.1%
Hungary -6.8% Finland 4.9%
Turkey -6.4% Germany 4.0%
United States -6.4% Japan 3.7%
Sources: Datastream/National sources.
24
Table 2: Summary statistics (based on quarterly data)
Mean Autocorrelation at lag:
Variable (of absolute values) 4 8 12 20
net exports/GDP 2.7% 0.76 0.64 0.55 0.47
current account/GDP 3.1% 0.77 0.68 0.58 0.53
Sources: Datastream/National sources and OECD.
Computations based on data for 18 OECD countries. The sample period covers
1957:01-2005:03.
Table 3: Benchmark parameter values
Preferences β = .99, γ = 2
Technology α = .36, δ = .025
Productivity process Λ =
[
.906 .088
.088 .906
]
Σ = .008522 ×[
1 0.258
0.258 1
]
Table 4: Average annual t.f.p. growth rates across G7 countries (in %)
1970-80 1980-90 1990-00 2000-05
United States 0.76 0.78 1.49 1.36
Canada 0.74 0.50 1.11 0.91
United Kingdom - 1.03 1.37 1.02
France - 1.22 0.78 0.90
Germany 2.11 1.09 1.13 0.86
Italy 3.86 1.35 0.93 -0.56
Japan - 1.38 0.42 1.44
Source: OECD, authors’ calculations.
25
Table 5: Average annual per capita GDP growth rates across G7 countries (in %)
1960-701 1970-80 1980-90 1990-00 2000-04
United States 2.89 2.21 2.11 1.98 1.43
Canada 3.32 2.60 1.69 1.53 1.80
United Kingdom 2.24 2.25 2.16 1.99 2.25
France 3.42 2.97 1.70 1.47 1.33
Germany 3.49 2.82 1.72 0.85 0.73
Italy 4.62 5.16 2.16 1.37 0.87
Japan 9.07 3.50 3.23 1.00 1.24
1France: 1963-1970. Source: OECD.
Table 6: Different parametrization of the technology process
Parametrization 1 σz = τ = 0.006, λ = 1/20 (on average technological changes
happen every 5 years)
Parametrization 2 σz = 0.5τ = 0.0043, λ = 1/20
Parametrization 3 σz = τ = 0.006, λ = 1/40 (on average technological changes
happen every 10 years)
Parametrization 4 σz = 0.5τ = 0.0043, λ = 1/40
26
Figure 1: External deficits since 1960
−.1
0.1
.2R
atio
of N
et E
xpor
ts to
GD
P
1960 1970 1980 1990 2000 2010Year
−.1
0.1
.2R
atio
of C
urre
nt A
ccou
nt to
GD
P
1960 1970 1980 1990 2000 2010Year
The data cover 18 OECD countries: Australia, Austria, Canada, Denmark, Finland,France, Germany, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Swe-den, Switzerland, United Kingdom and the United States.
27
Figure 2: Persistence of net exports and current accounts
−.2
−.1
0.1
.24
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Net Exports to GDP
−.2
−.1
0.1
.28
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Net Exports to GDP
−.2
−.1
0.1
.212
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Net Exports to GDP
−.2
−.1
0.1
.220
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Net Exports to GDP
−.2
−.1
0.1
.24
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Current Account to GDP
−.2
−.1
0.1
.28
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Current Account to GDP
−.2
−.1
0.1
.212
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Current Account to GDP
−.2
−.1
0.1
.220
Qua
rter
s A
head
−.2 −.1 0 .1 .2Ratio of Current Account to GDP
Quarterly data for 18 OECD countries: Australia, Austria, Canada, Denmark, Finland,France, Germany, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Swe-den, Switzerland, United Kingdom and the United States.
28
Figure 3: Current account balance/GDP
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Canada, n=195
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6Periodogram: Canada
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: Canada
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: France, n=75
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5Periodogram: France
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: France
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Germany, n=59
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2Periodogram: Germany
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1Spectrum: Germany
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Italy, n=131
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5Periodogram: Italy
0 0.1 0.2 0.3 0.4 0.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8Spectrum: Italy
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Japan, n=82
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5Periodogram: Japan
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1Spectrum: Japan
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: UK, n=195
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5
3
3.5
4Periodogram: UK
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: UK
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: US, n=183
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6Periodogram: US
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: US
29
Figure 4: Net exports/GDP
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Canada, n=179
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5Periodogram: Canada
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: Canada
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: France, n=110
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6
7
8Periodogram: France
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: France
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Germany, n=59
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5Periodogram: Germany
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: Germany
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Italy, n=103
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5Periodogram: Italy
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: Italy
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: Japan, n=103
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2Periodogram: Japan
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: Japan
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: UK, n=195
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5
2
2.5
3
3.5
4Periodogram: UK
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: UK
0 10 20 30 40 50
−1
−0.5
0
0.5
1
ACF: US, n=195
0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6Periodogram: US
0 0.1 0.2 0.3 0.4 0.50
0.5
1
1.5Spectrum: US
30
Figure 5: Spectrum of net exports/GDP implied by the benchmark model
0 10 20 30 40 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
Figure 6: Impulse response functions to a 1% productivity shock in country 1
(benchmark model)
0 10 20 30 40 500
0.002
0.004
0.006
0.008
0.01technology
z1z2
0 10 20 30 40 500.995
1
1.005
1.01
1.015output
y1y2
0 10 20 30 40 50−0.4
−0.2
0
0.2
0.4net investment
ni1ni2
0 10 20 30 40 501
1.002
1.004
1.006
1.008consumption
0 10 20 30 40 50−0.1
−0.05
0
0.05
0.1net exports/GDP
nx1nx2
31
Figure 7: Spectrum of net exports/GDP implied by an incomplete markets model
with Backus et al. (1992) calibration
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
Figure 8: Spectrum of productivity and per capita GDP differences US/OECD
aggregate
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Productivity differences
0 0.1 0.2 0.3 0.4 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Per capita GDP differences
32
Figure 9: Spectrum of productivity differences for the different parameterizations
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
1.5Parameterization 1
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
1.5Parameterization 2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
1.5Parameterization 3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.5
1
1.5Parameterization 4
33
Figure 10: ACF and spectrum of net exports/GDP for the different parameteriza-
tions
Parametrization 1
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
Parametrization 2
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
Parametrization 3
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
Parametrization 4
0 5 10 15 20 25 30 35 40 45 50
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
ACF
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
0.2
0.4
0.6
0.8
1
1.2
1.4Spectrum
34
Figure 11: Spectrum of per capita GDP differences for the different parameteriza-