This appendix presents several robustness experiments, carried on actual and simulated data.

Martial Dupaigne

Patrick Feve

English

Research Papers in Economics

Appendix to `Technology shocks around the world'I
Martial Dupaignea,b, Patrick F evea,c,d,e
aToulouse School of Economics (GREMAQ), 21 all ee de Brienne, F-31000 Toulouse, France
bUniversity of Western Brittany, Brest, France
cInstitut d' Economie Industrielle, Toulouse, France
dInstitut Universitaire de France
eBanque de France, Research Division
Abstract
This appendix presents several robustness experiments, carried on actual and simulated
data.
Key words: Technology shocks, Labor input, Vector Autoregressions, Multi{country
economy.
A. Robustness of empirical results
We now assess the robustness of the empirical ndings presented in Section 1.3 of the
main text. We consider larger SVAR models and a more exhaustive measure of labor
input.
A.1. Larger SVAR models
In what follows, we systematically compare the results of larger VARs to the responses
obtained in Section 1.3 with aggregate{level labor productivity.
First, we include in ~ Zt an additional variable, the dierence between the country{
level labor productivity and the G7 aggregate labor productivity. Since a single stochastic
trend hits permanently the seven country{level labor productivities, the labor produc-
tivity dierentials xi;t   xG7;t (i = 1;:::;7) help to capture persistent country{specic
components in labor productivities.
The results of this experiment are reported in Figure 8. For each country, the left
panel displays the IRF of employment to a permanent productivity shock (thick grey
line) in a VAR (xG7;ni;xi   xG7), as well as the estimated IRF of Figure 3 (from
the main text) with its 95% condence interval. The right panel displays two smoothed
distributions of impact responses: the light grey one refers to VAR (xG7;ni), as in
Figure 3; the medium grey one refers to VAR (xG7;ni;xi   xG7).
IThe views expressed therein are those of the authors and do not necessarily reect those of the
Banque de France.
Email addresses: martial.dupaigne@univ-tlse1.fr (Martial Dupaigne),
patrick.feve@univ-tlse1.fr (Patrick F eve)
Preprint submitted to Elsevier December 19, 2008The response of employment in US, Canada Japan and France in the three-variables
VAR are very similar to those obtained with the two-variables VAR. In two continental
European countries (Germany and Italy), the addition of productivity dierentials in
the VAR slightly shifts up the responses of labor input. In UK, it shifts them down.
The discrepancy between the results of the two VAR models suggest that these three
countries have a persistent country{specic component in labor productivity.
Second, we include in ~ Zt the seven country{level labor inputs: ~ Zt = (xG7;t;n1;t;:::;n7;t)
0.
This specication captures in a single SVAR model the joint dynamics of employment
in the major seven countries. The estimated responses are displayed in Figure 9. For all
countries, the results established in the two{variables VAR are preserved in this eight{
variables VAR.
A.2. Hours worked data
As emphasized by Gal  (2005), the choice between the dierent measures of labor in-
put available may have some consequences on the identication of permanent technology
shocks. We now use hours worked rather than employment to ensure that (potential)
permanent shocks to hours per worker do not have long{run eects on our measure of
labor productivity.
In the OECD countries, hours per worker are only available at annual frequency for
relatively long homogenous time series. Hours worked are dened as the product of
civilian employment and hours per employee, subsequently converted per capita. Labor
productivity is here dened as real output per hour worked. We evaluate the response
of hours worked at annual frequency over the sample 1972-2004.
We perform two estimations with this annual dataset. First, we compute the IRFs
of hours worked using country{level data. Second, we replace country{level labor pro-
ductivity by G7 aggregate labor productivity. Figure 10 reports the results of the two
experiments.1 The left panel displays the IRFs of hours worked in each country while
the right panel reports empirical distributions.
We nd the same pattern with hours worked data and with employment data: when
we use G7 labor productivity instead of country{level ones, IRFs shift up and the em-
pirical distribution of impact responses moves on the right for most countries. A sharp
distinction between US, Canada and UK, on one side, and continental European countries
plus Japan, on the other side, emerges. The rst group exhibits large responsiveness of
hours worked to technology shocks, whereas the second group features small adjustment.
When we use country{level labor productivity, an aggregation anomaly occurs with
hours worked data as it does with employment data. The weighted sum of country{
level point estimates is negative and lies outside the condence interval around the G7
aggregate response. For instance, the country{level based impact response equals -0.368,
while the impact response obtained at the aggregate level is 0.254. When G7 labor
productivity is used instead of country{level labor productivities, the weighted sum of
impact responses becomes 0.251.
1We report the 90% condence interval, as compared to 95% interval for quarterly data, to take into
account the lack of precision due to the short annual sample.
2Figure 8: IRFs of employment to an aggregate{level permanent productivity shock in larger VARs {
Productivity dierentials
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
USA
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
USA
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
CAN
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
CAN
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
JPN
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
JPN
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
GBR
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
GBR
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
DEU
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
DEU
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
FRA
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
FRA
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
ITA
−1.5 −1 −0.5 0 0.5 1
0
1
2
3
4
5
6
7
8
ITA
Note: For each country, the left panel displays the impulse response function of employ-
ment to a permanent productivity shock in a VAR (xG7;ni;xi   xG7) (black thick
line), as well as the point estimate impulse response of Figure 3 and its 95% condence
interval. The right panel displays two smoothed distributions of impact responses ob-
tained by standard bootstrap techniques, using 1000 draws from the sample residuals:
the light grey one refers to VAR (xG7;ni), as in Figure 3; the medium grey one refers
to VAR (xG7;ni;xi   xG7).
3Figure 9: IRFs of employment to an aggregate{level permanent productivity shock in larger VARs {
Seven countries' labor inputs
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
USA
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
USA
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
CAN
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
CAN
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
JPN
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
JPN
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
GBR
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
GBR
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
DEU
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
DEU
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
FRA
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
FRA
2 4 6 8 10 12
−0.5
0
0.5
1
1.5
2
ITA
−0.5 0 0.5
0
1
2
3
4
5
6
7
8
9
ITA
Note: For each country, the left panel displays the impulse response function of employ-
ment to a permanent productivity shock in a VAR
 
xG7;ni;n i
(black thick line),
as well as the point estimate impulse response of Figure 3 and its 95% condence inter-
val. The right panel displays two smoothed distributions of impact responses obtained
by standard bootstrap techniques, using 1000 draws from the sample residuals: the light
grey one refers to VAR (xG7;ni), as in Figure 3; the medium grey one refers to VAR  
xG7;ni;n i
.
4Figure 10: IRFs of hours worked to an aggregate{level permanent productivity shock on annual data
1 2 3 4 5
−3
−2
−1
0
1
2
3
USA
−4 −2 0 2 4
0
0.5
1
1.5
2
USA
1 2 3 4 5
−3
−2
−1
0
1
2
3
CAN
−4 −2 0 2 4
0
0.5
1
1.5
2
CAN
1 2 3 4 5
−3
−2
−1
0
1
2
3
JPN
−4 −2 0 2 4
0
0.5
1
1.5
2
JPN
1 2 3 4 5
−3
−2
−1
0
1
2
3
GBR
−4 −2 0 2 4
0
0.5
1
1.5
2
GBR
1 2 3 4 5
−3
−2
−1
0
1
2
3
DEU
−4 −2 0 2 4
0
0.5
1
1.5
2
DEU
1 2 3 4 5
−3
−2
−1
0
1
2
3
FRA
−4 −2 0 2 4
0
0.5
1
1.5
2
FRA
1 2 3 4 5
−3
−2
−1
0
1
2
3
ITA
−4 −2 0 2 4
0
0.5
1
1.5
2
ITA
1 2 3 4 5
−3
−2
−1
0
1
2
3
G7M
−4 −2 0 2 4
0
0.5
1
1.5
2
G7M
Note: For each country, the left panel displays the impulse response function of hours
worked to a permanent productivity shock in a two-lags VAR (xG7;ni) and its 90%
condence interval, as well as the point estimate impulse response of the VAR (xi;ni).
The right panel displays two smoothed distributions of impact responses obtained by
standard bootstrap techniques, using 1000 draws from the sample residuals: the light
grey one refers to VAR (xi;ni), as in Figure 1; the medium grey one refers to VAR
(xG7;ni).
5B. Estimation results with other datasets
We report in Table 7 ML estimations of the DSGE model with other datasets. We
rst replace the growth rate of US per capita output with the growth rate of US labor
productivity for the same sample (1959:1-2003:4) and for a shorter one (1978:1-2003:4).
Second we replace the growth rate of US labor productivity by the growth rate of G7
labor productivity (the latter data being available from 1978).
Table 7: Robustness of estimation results
US productivity growth G7 productivity growth
Estimated parameter 1959:1-2003:4 1978:1-2003:4 1978:1-2003:4
' 0.8511 1.0102 1.5781
(0.2417) (0.3432) (0.1861)
a 0.0176 0.0152 0.0105
(0.0012) (0.0015) (0.0007)
 0.9983 0.9975 0.9994
(0.0122) (0.0187) (0.0022)
! 0.0031 0.0032 0.0049
(0.0010) (0.0014) (0.0007)
 0.9229 0.9295 0.9668
(0.0405) (0.0446) (0.0126)
 0.0082 0.0074 0.0081
(0.0006) (0.0007) (0.0006)
Note: The vector of observed data includes the growth rates of labor productivity, the growth
rates of US hours worked and investment to output ratio. Standard{errors in parentheses.
C. Counterfactual experiments
Another way to understand how country{specic shocks contaminate the response
to a permanent TFP improvement is to shut down the international dimensions of the
model. We successively alter three margins: the relative volatilities of shocks, their
relative persistence and the size of the domestic economy.
In the rst counterfactual experiment, we decrease the standard error of both station-
ary shocks leaving unchanged the volatility of the common permanent shock. More pre-
cisely, we make the relative productivity shock and the preference shock half as volatile,
compute another set of S equilibrium paths and re-estimate the three structural VARs.
The implied response of labor input to the permanent productivity shock are displayed
in Figure 12.
The left panel of Figure 12 shows that the bias in the country{level experiment
is greatly reduced. An applied researcher would no longer reject the hypothesis that
these data have been generated by the theoretical model; nor would she reject that the
employment response is positive. The comparison of the left panels of Figure 6 and Figure
12 exemplies the contamination (or the lack thereof) of the domestic labor productivity
when SVARs with long{run restrictions are used to reveal permanent productivity shocks.
6The improved performance of the country{level SVAR model is a direct consequence of
the greater contribution of the world technology shock to domestic uctuations. It now
accounts for 91% of the variance of labor productivity after one quarter, and 58% of the
variance of labor input.
The middle and right panels of Figure 12 do conrm the ndings of Figure 6: the use
of aggregate labor productivity, instead of country{level labor productivity, shifts the
estimated response up towards the true response of employment. The experiment with
zone employment delivers virtually the same response as the experiment with domestic
employment, but with increased precision.
In a second experiment, we make stationary shocks half as persistent as in the bench-
mark. The responses of employment to the permanent shock estimated with the three
SVAR models are displayed in Figure 13.
The left panel, which corresponds to country{level articial data, shows that the
contamination of permanent productivity shocks is less acute when the other shocks are
less persistent. The middle and right panel exhibit the same pattern as before: the
use of aggregate{level labor productivity reduces the bias, while the best precision is
achieved with aggregate{level employment. Once again, this reduction in bias is a direct
consequence of a greater contribution of the world technology shock.
Another dimension in which the contamination of labor productivity is apparent is its
persistence. Figure 15 plots the theoretical autocorrelation function of the log{deviations
of labor productivity from trend, log(Yi;t)   log(Ni;t)   log(At). The left panel shows
that, in the benchmark model, deviations of the domestic labor productivity are much
more persistent than deviations of the zone labor productivity. The discrepancy is much
lower when the volatility of country{specic shocks is reduced (middle panel), and it
disappears completely when country{specic shocks have a low autocorrelation coecient
(right panel). Figure 15 hence conrms the insights of Figures 6 to 13: in our model of
the US economy, labor productivity persistently deviates from its stochastic trend and
these deviations perturb identication based on long{run restrictions. Aggregate{level
productivity is less distorted by persistent, non{permanent shocks.
Our third, and last, counterfactual experiment concerns the relative size of the do-
mestic economy, 1. The benchmark case portrays the US as home country, implying
1 = 0:40. The US has the largest population in the seven countries we consider in the
empirical analysis, while Canada has the lowest population share, 0.04. In the model,
the size of the domestic economy controls for its exposure to foreign shocks, as well as
for the distinction between the domestic economy and the zone economy.
Figure 14 plots the estimated response of employment for values of 1 between 0.05
and 0.8. The left panel shows that the response estimated in a VAR with country{level
data monotonously increases with the size of the domestic economy, reducing the bias.
As 1 goes from low values to 0.5, the contamination of domestic labor productivity
by the idiosyncratic productivity choice is reduced and eventually disappears. When
1 = 0:5, the only remaining contamination is due to the preference shock. For values
of 1 above 0.5, relative productivity shock do perturb again the identication of the
common permanent shock to TFP.
The remaining two experiments, displayed in the middle and right panel of Figure 14,
respectively, concern the SVAR on zone data and the SVAR combining aggregate{level
labor productivity with country{level employment. Those experiments illustrate that
the dierence between country{level and aggregate{level labor productivity is high for
7low values of 1 and disappears as 1 tends to unity. Hence, the estimated responses of
employment in the three VAR models are close when the domestic economy represents
a large share of world economy, as can be seen when 1 = 0:8.
Overall, our set of experiments yields a clear conclusion. When the contribution of
country{specic shocks is of the size observed on US data or larger, the response of
labor input to permanent technology improvements estimated using country{level data
is severely biased. The use of aggregate{level labor productivity instead of country{
level labor productivity shifts the estimated response towards their true value. These
quantitative results give strong support to the empirical analysis using G7{aggregates
put forward in this paper.
Figure 11: Estimated response of employment in the robustness experiments
2 4 6 8 10 12
−1
−0.5
0
0.5
1
2 4 6 8 10 12
−1
−0.5
0
0.5
1
1.5
2 4 6 8 10 12
−1.5
−1
−0.5
0
0.5
1
1.5
Domestic labor input Domestic labor input, Zone APL, domestic
and zone APL zone APL and and foreign labor input
productivity dierential
Note: VAR estimated on data generated by the two{country model with parameter values de-
scribed in Table 1 (S = 500 simulations of 104 observations), yielding the VMA representation
(6).
Figure 12: Estimated response of employment with less volatile shocks
2 4 6 8 10 12
−0.5
0
0.5
1
2 4 6 8 10 12
−0.5
0
0.5
1
2 4 6 8 10 12
−0.5
0
0.5
1
Domestic labor input Zone labor input Domestic labor input
and domestic APL and zone APL and zone APL
Note: VAR estimated on data generated by the two{country model with parameter values de-
scribed in Table 1 (S = 500 simulations of 104 observations), yielding the VMA representation
(6).
8Figure 13: Estimated response of employment with less persistent shocks
2 4 6 8 10 12
−0.5
0
0.5
1
2 4 6 8 10 12
−0.5
0
0.5
1
2 4 6 8 10 12
−0.5
0
0.5
1
Domestic labor input Zone labor input Domestic labor input
and domestic APL and zone APL and zone APL
Note: VAR estimated on data generated by the two{country model with parameter values de-
scribed in Table 1 (S = 500 simulations of 104 observations), yielding the VMA representation
(6).
Figure 14: Estimated response of employment according to the size of the `home' country
2 4 6 8 10 12
−0.4
−0.2
0
0.2
0.4
0.6
π=0.05 π=0.1
π=0.2
π=0.4
π=0.8
model
2 4 6 8 10 12
−0.4
−0.2
0
0.2
0.4
0.6
π=0.05
π=0.1π=0.2
π=0.4
π=0.8
model
2 4 6 8 10 12
−0.4
−0.2
0
0.2
0.4
0.6
π=0.05
π=0.1π=0.2π=0.4
π=0.8
model
Domestic labor input Zone labor input Domestic labor input
and domestic APL and zone APL and zone APL
Note: VAR estimated on data generated by the two{country model with parameter values de-
scribed in Table 1 (S = 500 simulations of 104 observations), yielding the VMA representation
(6).
Figure 15: Autocorrelation functions of labor productivity
0 5 10 15 20
0.4
0.5
0.6
0.7
0.8
0.9
1
Domestic APL
Zone APL
0 5 10 15 20
0.4
0.5
0.6
0.7
0.8
0.9
1
Domestic APL
Zone APL
0 5 10 15 20
0.4
0.5
0.6
0.7
0.8
0.9
1
Domestic APL
Zone APL
Benchmark Half as volatile Half as persistent
Note: Autocorrelation functions of labor productivity in deviation from the stochastic trend, as
implied by the two{country model with parameter values described in Table 1.
9

Online Appendix to "Technology shocks around the world"

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Online Appendix to "Technology shocks around the world"

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